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Van der Waals equation
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The van der Waals equation (or van der Waals equation of state; named after Johannes Diderik van der Waals) is based on plausible reasons that real gases do not follow the ideal gas law. The ideal gas law treats gas molecules as point particles that do not interact with each other but only the walls. In other words, they do not take up any space, and are not attracted or repelled by other gas molecules.[1] The Ideal Gas Law states that volume (V) occupied by n moles of any gas has a pressure (P) at temperature (T) in Kelvin. The relationship for these variables, P V = n R T, where R is known as the gas constant, is called the ideal gas law or equation of state.
To account for the volume that a real gas molecule takes up, the van der Waals equation replaces V in the ideal gas law with (V-b), where b is the volume per mole that is occupied by the molecules. This leads to:[1]
P ( V m − b ) = R T {\displaystyle P(V_{m}-b)=RT}
The second modification made to the ideal gas law accounts for the fact that gas molecules do in fact attract each other and that real gases are therefore more compressible than ideal gases. Van der Waals provided for intermolecular attraction by adding to the observed pressure P in the equation of state a term a / V m 2 {\displaystyle a/V_{m}^{2}} , where a is a constant whose value depends on the gas. The van der Waals equation is therefore written as:[1]
( P + a / V m 2 ) ( V m − b ) = R T {\displaystyle (P+a/V_{m}^{2})(V_{m}-b)=RT}
and can also be written as
( P + a n 2 / V 2 ) ( V − n b ) = n R T {\displaystyle (P+an^{2}/V^{2})(V-nb)=nRT}
where Vm is the molar volume of the gas, R is the universal gas constant, T is temperature, P is pressure, and V is volume. When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the van der Waals equation reduces to the ideal gas law, PVm=RT.[1]
It is available via its traditional derivation (a mechanical equation of state), or via a derivation based in statistical thermodynamics, the latter of which provides the partition function of the system and allows thermodynamic functions to be specified. It successfully approximates the behavior of real fluids above their critical temperatures and is qualitatively reasonable for their liquid and low-pressure gaseous states at low temperatures. However, near the transitions between gas and liquid, in the range of p, V, and T where the liquid phase and the gas phase are in equilibrium, the van der Waals equation fails to accurately model observed experimental behaviour, in particular that p is a constant function of V at given temperatures. As such, the van der Waals model is not useful only for calculations intended to predict real behavior in regions near the critical point. Empirical corrections to address these predictive deficiencies have been inserted into the van der Waals model, e.g., by James Clerk Maxwell in his equal area rule, and related but distinct theoretical models, e.g., based on the principle of corresponding states, have been developed to achieve better fits to real fluid behaviour in equations of comparable complexity.
Contents
1 Overview and history
2 Equation
2.1 Reduced form
3 Validity
4 Derivation
4.1 Conventional derivation
4.2 Statistical thermodynamics derivation
5 Maxwell equal area rule
5.1 From chemical potential
6 Other parameters, forms and applications
6.1 Other thermodynamic parameters
6.2 Reduced form
6.3 Cubic equation
6.4 Application to compressible fluids
7 See also
8 References
9 Further reading
10 External links
Overview and history[edit]
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The van der Waals equation is a thermodynamic equation of state based on the theory that fluids are composed of particles with non-zero volumes, and subject to a (not necessarily pairwise) inter-particle attractive force.[citation needed] It was based on work in theoretical physical chemistry performed in the late 19th century by Johannes Diderik van der Waals, who did related work on the attractive force that also bears his name.[citation needed] The equation is known to be based on a traditional set of derivations deriving from van der Waals' and related efforts,[citation needed] as well as a set of derivation based in statistical thermodynamics,[citation needed] see below.
Van der Waals' early, primary interests were in the field of thermodynamics, where a first influence was the published work by Rudolf Clausius on heat, in 1857; other significant influences were the writings by James Clerk Maxwell, Ludwig Boltzmann, and Willard Gibbs.[2] After initial pursuit of teaching credentials, van der Waals' undergraduate coursework in mathematics and physics at the University of Leiden in the Netherlands led, with significant hurdles, to his acceptance for doctoral studies at Leiden under Pieter Rijke. While his dissertation helps to explain the experimental observation in 1869 by Irish professor of chemistry Thomas Andrews (Queen's University Belfast) of the existence of a critical point in fluids[3], science historian Martin J. Klein states that it is not clear whether van der Waals was aware of Andrews' results when he began his doctorate work[4]. Van der Waals' doctoral research culminated in an 1873 dissertation that provided a semi-quantitative theory describing the gas-liquid change of state and the origin of a critical temperature, Over de Continuïteit van den Gas-en Vloeistof[-]toestand (Dutch; in English, On the Continuity of the Gas- and Liquid-State); it was in this dissertation that the first derivations of what we now refer to as the van der Waals equation appeared.[5] James Clerk Maxwell reviewed and lauded its published content in the British science journal Nature,[6][7] and van der Waals began independent work that would result in his receipt of the Nobel Prize in 1910, which emphasized the contribution of his formulation of this "equation of state for gases and liquids."[2]
Equation[edit]
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van der Waals isotherms.[citation needed] The model correctly predicts a mostly incompressible liquid phase, but the oscillations in the phase transition zone do not fit experimental data.
van der Waals isotherms and oscillations, temperatures, T, below and above TC.[citation needed] Shown in this PV diagram are a series of 5 isotherms for temperatures ranging from below (blue) to above (red) TC, where the upward arise and downward dip in the isotherm predicted by the van der Waals equation (the "oscillation," especially evident for the two isotherms for values of T < TC) is evident in the region of the gas-liquid phase transition.
The equation relates four state variables: the pressure of the fluid p, the total volume of the fluid's container V, the number of particles N, and the absolute temperature of the system T.
The intensive, microscopic form of the equation is:
( p + a ′ v 2 ) ( v − b ′ ) = k T {\displaystyle \left(p+{\frac {a'}{v^{2}}}\right)\left(v-b'\right)=kT} [2]
where
v = V / N {\displaystyle v=V/N}
is the volume of the container occupied by each particle (not the velocity of a particle), and k is the Boltzmann constant. It introduces two new parameters: a', a measure of the average attraction between particles, and b', the volume excluded from v by one particle.
The equation can be also written in extensive, molar form:
( p + n 2 a V 2 ) ( V − n b ) = n R T {\displaystyle \left(p+{\frac {n^{2}a}{V^{2}}}\right)\left(V-nb\right)=nRT} [8]
where
a = N A 2 a ′ {\displaystyle a=N_{A}^{2}a'}
is a measure of the average attraction between particles,
b = N A b ′ {\displaystyle b=N_{A}b'}
is the volume excluded by a mole of particles,
n = N / N A {\displaystyle n=N/N_{A}}
is the number of moles,
R = N A k {\displaystyle R=N_{A}k}
is the universal gas constant, k is Boltzmann's constant, and NA is Avogadro's constant.
A careful distinction must be drawn between the volume available to a particle and the volume of a particle.[according to whom?] In the intensive equation, v equals the total space available to each particle, while the parameter b' is proportional to the proper volume of a single particle - the volume bounded by the atomic radius. This is subtracted from v because of the space taken up by one particle.[citation needed] In van der Waals' original derivation, given below, b' is four times the proper volume of the particle. Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb.[9][self-published source?][better source needed]
Reduced form[edit]
The van der Waals equation can also be expressed in terms of reduced properties:
( P r + 3 V r 2 ) ( v r − 1 3 ) = 8 3 T {\displaystyle \left(P_{r}+{\frac {3}{V_{r}^{2}}}\right)\left(v_{r}-{\frac {1}{3}}\right)={\frac {8}{3}}T}
This yields a critical compressibility factor of 3/8.
Validity[edit]
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The van der Waals equation is mathematically simple, but it nevertheless predicts the experimentally observed transition between vapor and liquid, and predicts critical behaviour.[10]:289
Above the critical temperature, TC, the van der Waals equation is an improvement over the ideal gas law, and for lower temperatures, i.e., T < TC, the equation is also qualitatively reasonable for the liquid and low-pressure gaseous states; however, with respect to the first-order phase transition, i.e., the range of (p, V, T) where a liquid phase and a gas phase would be in equilibrium, the equation appears to fail to predict observed experimental behaviour, in the sense that p is typically observed to be constant as a function of V for a given temperature in the two-phase region. This apparent discrepancy is resolved in the context of vapour–liquid equilibrium: at a particular temperature, there exist two points on the van der Waals isotherm that have the same chemical potential, and thus a system in thermodynamic equilibrium will appear to traverse a straight line on the p–V diagram as the ratio of vapour to liquid changes. However, in such a system, there are really only two points present (the liquid and the vapour) rather than a series of states connected by a line, so connecting the locus of points is incorrect: it is not an equation of multiple states, but an equation of (a single) state. It is indeed possible to compress a gas beyond the point at which it would typically condense, given the right conditions, and it is also possible to expand a liquid beyond the point at which it would usually boil. Such states are called "metastable" states. Such behaviour is qualitatively (though perhaps not quantitatively) predicted by the van der Waals equation of state.[11]
However, the values of physical quantities as predicted with the van der Waals equation of state "are in very poor agreement with experiment," so the model's utility is limited to qualitative rather than quantitative purposes.[10]:289 Empirically-based corrections can easily be inserted into the van der Waals model (see Maxwell's correction, below), but in so doing, the modified expression is no longer as simple an analytical model; in this regard, other models, such as those based on the principle of corresponding states, achieve a better fit with roughly the same work.[citation needed] Even with its acknowledged shortcomings, the pervasive use of the van der Waals equation in standard university physical chemistry textbooks makes clear its importance as a pedagogic tool to aid understanding fundamental physical chemistry ideas involved in developing theories of vapour–liquid behavior and equations of state.[12][13][14] In addition, other (more accurate) equations of state such as the Redlich–Kwong and Peng–Robinson equation of state are essentially modifications of the van der Waals equation of state.
Derivation[edit]
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Textbooks in physical chemistry generally give two derivations of the title equation.[who?] One is the conventional derivation that goes back to van der Waals, a mechanical equation of state that cannot be used to specify all thermodynamic functions; the other is a statistical mechanics derivation that makes explicit the intermolecular potential neglected in the first derivation.[citation needed] A particular advantage of the statistical mechanical derivation is that it yields the partition function for the system, and allows all thermodynamic functions to be specified (including the mechanical equation of state).[citation needed]
Conventional derivation[edit]
Consider one mole of gas composed of non-interacting point particles that satisfy the ideal gas law:(see any standard Physical Chemistry text, op. cit.)
p = R T V m = R T v . {\displaystyle p={\frac {RT}{V_{\mathrm {m} }}}={\frac {RT}{v}}.}
Next, assume that all particles are hard spheres of the same finite radius r (the van der Waals radius). The effect of the finite volume of the particles is to decrease the available void space in which the particles are free to move. We must replace V by V − b, where b is called the excluded volume or "co-volume". The corrected equation becomes
p = R T V m − b . {\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}.}
The excluded volume b {\displaystyle b} is not just equal to the volume occupied by the solid, finite-sized particles, but actually four times that volume. To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original radius) that is forbidden for the centers of the other particles. If the distance between two particle centers were to be smaller than 2r, it would mean that the two particles penetrate each other, which, by definition, hard spheres are unable to do.
The excluded volume for the two particles (of average diameter d or radius r) is
b 2 ′ = 4 π d 3 / 3 = 8 × ( 4 π r 3 / 3 ) {\displaystyle b'_{2}=4\pi d^{3}/3=8\times (4\pi r^{3}/3)} ,
which, divided by two (the number of colliding particles), gives the excluded volume per particle:
b ′ = b 2 ′ / 2 → b ′ = 4 × ( 4 π r 3 / 3 ) {\displaystyle b'=b'_{2}/2\quad \rightarrow \quad b'=4\times (4\pi r^{3}/3)} ,
So b′ is four times the proper volume of the particle. It was a point of concern to van der Waals that the factor four yields an upper bound; empirical values for b′ are usually lower. Of course, molecules are not infinitely hard, as van der Waals thought, and are often fairly soft.
Next, we introduce a (not necessarily pairwise) attractive force between the particles. van der Waals assumed that, notwithstanding the existence of this force, the density of the fluid is homogeneous; furthermore, he assumed that the range of the attractive force is so small that the great majority of the particles do not feel that the container is of finite size.[citation needed] Given the homogeneity of the fluid, the bulk of the particles do not experience a net force pulling them to the right or to the left. This is different for the particles in surface layers directly adjacent to the walls. They feel a net force from the bulk particles pulling them into the container, because this force is not compensated by particles on the side where the wall is (another assumption here is that there is no interaction between walls and particles, which is not true, as can be seen from the phenomenon of droplet formation; most types of liquid show adhesion). This net force decreases the force exerted onto the wall by the particles in the surface layer. The net force on a surface particle, pulling it into the container, is proportional to the number density
C = N A / V m {\displaystyle C=N_{\mathrm {A} }/V_{\mathrm {m} }} .
The number of particles in the surface layers is, again by assuming homogeneity, also proportional to the density. In total, the force on the walls is decreased by a factor proportional to the square of the density, and the pressure (force per unit surface) is decreased by
a ′ C 2 = a ′ ( N A V m ) 2 = a V m 2 {\displaystyle a'C^{2}=a'\left({\frac {N_{\mathrm {A} }}{V_{\mathrm {m} }}}\right)^{2}={\frac {a}{V_{\mathrm {m} }^{2}}}} ,
so that
p = R T V m − b − a V m 2 ⇒ ( p + a V m 2 ) ( V m − b ) = R T . {\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}-{\frac {a}{V_{\mathrm {m} }^{2}}}\Rightarrow \left(p+{\frac {a}{V_{\mathrm {m} }^{2}}}\right)(V_{\mathrm {m} }-b)=RT.}
Upon writing n for the number of moles and nVm = V, the equation obtains the second form given above,
( p + n 2 a V 2 ) ( V − n b ) = n R T . {\displaystyle \left(p+{\frac {n^{2}a}{V^{2}}}\right)(V-nb)=nRT.}
It is of some historical interest to point out that van der Waals, in his Nobel prize lecture, gave credit to Laplace for the argument that pressure is reduced proportional to the square of the density.[citation needed]
Statistical thermodynamics derivation[edit]
The canonical partition function Z of an ideal gas consisting of N = nNA identical (non-interacting) particles, is:[15][16]
Z = z N N ! with z = V Λ 3 {\displaystyle Z={\frac {z^{N}}{N!}}\quad {\hbox{with}}\quad z={\frac {V}{\Lambda ^{3}}}}
where Λ {\displaystyle \Lambda } is the thermal de Broglie wavelength,
Λ = h 2 2 π m k T {\displaystyle \Lambda ={\sqrt {\frac {h^{2}}{2\pi mkT}}}}
with the usual definitions: h is Planck's constant, m the mass of a particle, k Boltzmann's constant and T the absolute temperature. In an ideal gas z is the partition function of a single particle in a container of volume V. In order to derive the van der Waals equation we assume now that each particle moves independently in an average potential field offered by the other particles. The averaging over the particles is easy because we will assume that the particle density of the van der Waals fluid is homogeneous. The interaction between a pair of particles, which are hard spheres, is taken to be
u ( r ) = { ∞ when r < d , − ϵ ( d r ) 6 when r ≥ d , {\displaystyle u(r)={\begin{cases}\infty &{\hbox{when}}\quad r<d,\\-\epsilon \left({\frac {d}{r}}\right)^{6}&{\hbox{when}}\quad r\geq d,\end{cases}}}
r is the distance between the centers of the spheres and d is the distance where the hard spheres touch each other (twice the van der Waals radius). The depth of the van der Waals well is ϵ {\displaystyle \epsilon } .
Because the particles are not coupled under the mean field Hamiltonian, the mean field approximation of the total partition function still factorizes,
Z = z N / N ! {\displaystyle Z=z^{N}/N!} ,
but the intermolecular potential necessitates two modifications to z. First, because of the finite size of the particles, not all of V is available, but only V − Nb', where (just as in the conventional derivation above)
b ′ = 2 π d 3 / 3 {\displaystyle b'=2\pi d^{3}/3} .
Second, we insert a Boltzmann factor exp[ - ϕ/2kT] to take care of the average intermolecular potential. We divide here the potential by two because this interaction energy is shared between two particles. Thus
z = ( V − N b ′ ) e − ϕ / ( 2 k T ) Λ 3 . {\displaystyle z={\frac {(V-Nb')\,e^{-\phi /(2kT)}}{\Lambda ^{3}}}.}
The total attraction felt by a single particle is
ϕ = ∫ d ∞ u ( r ) N V 4 π r 2 d r , {\displaystyle \phi =\int _{d}^{\infty }u(r){\frac {N}{V}}4\pi r^{2}dr,}
where we assumed that in a shell of thickness dr there are N/V 4π r2dr particles. This is a mean field approximation; the position of the particles is averaged. In reality the density close to the particle is different than far away as can be described by a pair correlation function. Furthermore, it is neglected that the fluid is enclosed between walls. Performing the integral we get
ϕ = − 2 a ′ N V with a ′ = ϵ 2 π d 3 3 = ϵ b ′ . {\displaystyle \phi =-2a'{\frac {N}{V}}\quad {\hbox{with}}\quad a'=\epsilon {\frac {2\pi d^{3}}{3}}=\epsilon b'.}
Hence, we obtain,
ln  Z = N ln  ( V − N b ′ ) + N 2 a ′ V k T − N ln  ( Λ 3 ) − ln  N ! {\displaystyle \ln Z=N\ln {(V-Nb')}+{\frac {N^{2}a'}{VkT}}-N\ln {(\Lambda ^{3})}-\ln {N!}}
From statistical thermodynamics we know that
p = k T ∂ ln  Z ∂ V {\displaystyle p=kT{\frac {\partial \ln Z}{\partial V}}} ,
so that we only have to differentiate the terms containing V. We get
p = N k T V − N b ′ − N 2 a ′ V 2 ⇒ ( p + N 2 a ′ V 2 ) ( V − N b ′ ) = N k T ⇒ ( p + n 2 a V 2 ) ( V − n b ) = n R T . {\displaystyle p={\frac {NkT}{V-Nb'}}-{\frac {N^{2}a'}{V^{2}}}\Rightarrow \left(p+{\frac {N^{2}a'}{V^{2}}}\right)(V-Nb')=NkT\Rightarrow \left(p+{\frac {n^{2}a}{V^{2}}}\right)(V-nb)=nRT.}
Maxwell equal area rule[edit]
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Main article: Maxwell construction
van der Waals isotherm oscillation and Maxwell's equal areas.[17] Maxwell's rule eliminates the oscillating behavior of the isotherm in the phase transition zone by defining it as a certain isobar in that zone. The above isotherm is for a reduced temperature of TR=0.9. The Maxwell correction is at a vapor pressure of pV≈0.64700 between the reduced volume of the pure liquid VL≈0.60340 and the pure gas VG≈2.3488 at the vapor pressure.
Below the critical temperature, the van der Waals equation seems to predict qualitatively incorrect relationships. Unlike for ideal gases, the p-V isotherms oscillate with a relative minimum (d) and a relative maximum (e). Any pressure between pd and pe appears to have 3 stable volumes, contradicting the experimental observation that two state variables completely determine a one-component system's state.[17] Moreover, the isothermal compressibility is negative between d and e (equivalently ( ∂ P / ∂ V ) T , N > 0 {\displaystyle \scriptstyle \left({{\partial P}/{\partial V}}\right)_{T,N}>0} ), which cannot describe a system at equilibrium.[18]
To address these problems, James Clerk Maxwell replaced the isotherm between points a and c with a horizontal line positioned so that the areas of the two shaded regions would be equal (replacing the a-d-b-e-c curve with a straight line from a to c); this portion of the isotherm corresponds to the liquid-vapor equilibrium. The regions of the isotherm from a–d and from c–e are interpreted as metastable states of super-heated liquid and super-cooled vapor, respectively.[19] [20] The equal area rule can be expressed as:
p V ( V G − V L ) = ∫ V L V G p d V {\displaystyle p_{V}(V_{G}-V_{L})=\int _{V_{L}}^{V_{G}}p\,dV}
where pV is the vapor pressure (flat portion of the curve), VL is the volume of the pure liquid phase at point a on the diagram, and VG is the volume of the pure gas phase at point c on the diagram.[citation needed] A two-phase mixture at pV will occupy a total volume between VL and VG, as determined by Maxwell's lever rule.
Maxwell justified the rule based on the fact that the area on a pV diagram corresponds to mechanical work, saying that work done on the system in going from c to b should equal work released on going from a to b. This is because the change in free energy A(T,V) equals the work done during a reversible process, and, as a state variable, the free energy must be path-independent. In particular, the value of A at point b should be the same regardless of whether the path taken is from left or right across the horizontal isobar, or follows the original van der Waals isotherm.[citation needed]
This derivation is not entirely rigorous, since it requires a reversible path through a region of thermodynamic instability, while b is unstable.[clarification needed][citation needed] Nevertheless, modern derivations from chemical potential reach the same conclusion, and it remains a necessary modification to the van der Waals and to any other analytic equation of state.[17]
From chemical potential[edit]
The Maxwell equal area rule can also be derived from an assumption of equal chemical potential μ of coexisting liquid and vapour phases.[21][non-primary source needed] On the isotherm shown in the above plot, points a and c are the only pair of points which fulfill the equilibrium condition of having equal pressure, temperature and chemical potential. It follows that systems with volumes intermediate between these two points will consist of a mixture of the pure liquid and gas with specific volumes equal to the pure liquid and gas phases at points a and c.
The van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV.[citation needed] Since:[according to whom?]
p = − ( ∂ A ∂ V ) T , N {\displaystyle p=-\left({\frac {\partial A}{\partial V}}\right)_{T,N}}
where A is the Helmholtz free energy, it follows that the equal area rule can be expressed as:
p V = A ( V L , T , N ) − A ( V G , T , N ) V G − V L {\displaystyle p_{V}={\frac {A(V_{L},T,N)-A(V_{G},T,N)}{V_{G}-V_{L}}}} is
Since the gas and liquid volumes are functions of pV and T only, this equation is then solved numerically to obtain pV as a function of temperature (and number of particles N), which may then be used to determine the gas and liquid volumes.[citation needed]

Locus of coexistence for two phases of van der Waals fluid
A pseudo-3D plot of the locus of liquid and vapor volumes versus temperature and pressure is shown in the accompanying figure. One sees that the two locii meet at the critical point (1,1,1) smoothly. An isotherm of the van der Waals fluid taken at T r = 0.90 is also shown where the intersections of the isotherm with the loci illustrate the construct's requirement that the two areas (red and blue, shown) are equal.
Other parameters, forms and applications[edit]
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Other thermodynamic parameters[edit]
We reiterate that the extensive volume V is related to the volume per particle v=V/N where N = nNA is the number of particles in the system. The equation of state does not give us all the thermodynamic parameters of the system. We can take the equation for the Helmholtz energy A [22][self-published source?][better source needed]
A = − k T ln  Q . {\displaystyle A=-kT\ln Q.\,}
From the equation derived above for lnQ, we find
A ( T , V , N ) = − N k T [ 1 + ln  ( ( V − N b ′ ) T 3 / 2 N Φ ) ] − a ′ N 2 V . {\displaystyle A(T,V,N)=-NkT\left[1+\ln \left({\frac {(V-Nb')T^{3/2}}{N\Phi }}\right)\right]-{\frac {a'N^{2}}{V}}.}
Where Φ is an undetermined constant, which may be taken from the Sackur–Tetrode equation for an ideal gas to be:
Φ = T 3 / 2 Λ 3 = ( h 2 π m k ) 3 {\displaystyle \Phi =T^{3/2}\Lambda ^{3}=\left({\frac {h}{\sqrt {2\pi mk}}}\right)^{3}}
This equation expresses A in terms of its natural variables V and T , and therefore gives us all thermodynamic information about the system. The mechanical equation of state was already derived above
p = − ( ∂ A ∂ V ) T = N k T V − N b ′ − a ′ N 2 V 2 . {\displaystyle p=-\left({\frac {\partial A}{\partial V}}\right)_{T}={\frac {NkT}{V-Nb'}}-{\frac {a'N^{2}}{V^{2}}}.}
The entropy equation of state yields the entropy (S )
S = − ( ∂ A ∂ T ) V = N k [ ln  ( ( V − N b ′ ) T 3 / 2 N Φ ) + 5 2 ] {\displaystyle S=-\left({\frac {\partial A}{\partial T}}\right)_{V}=Nk\left[\ln \left({\frac {(V-Nb')T^{3/2}}{N\Phi }}\right)+{\frac {5}{2}}\right]}
from which we can calculate the internal energy
U = A + T S = 3 2 N k T − a ′ N 2 V . {\displaystyle U=A+TS={\frac {3}{2}}\,NkT-{\frac {a'N^{2}}{V}}.}
Similar equations can be written for the other thermodynamic potential and the chemical potential, but expressing any potential as a function of pressure p will require the solution of a third-order polynomial, which yields a complicated expression. Therefore, expressing the enthalpy and the Gibbs energy as functions of their natural variables will be complicated.
Reduced form[edit]
Although the material constant a and b in the usual form of the van der Waals equation differs for every single fluid considered, the equation can be recast into an invariant form applicable to all fluids.
Defining the following reduced variables (fR, fC are the reduced and critical variable versions of f, respectively),
p R = p p C , v R = v v C , and T R = T T C {\displaystyle p_{R}={\frac {p}{p_{C}}},\qquad v_{R}={\frac {v}{v_{C}}},\quad {\hbox{and}}\quad T_{R}={\frac {T}{T_{C}}}} ,
where
p C = a ′ 27 b ′ 2 , v C = 3 b ′ , and k T C = 8 a ′ 27 b ′ {\displaystyle p_{C}={\frac {a'}{27b'^{2}}},\qquad \displaystyle {v_{C}=3b'},\quad {\hbox{and}}\quad kT_{C}={\frac {8a'}{27b'}}}
as shown by Salzman.[23][self-published source?][better source needed]
The first form of the van der Waals equation of state given above can be recast in the following reduced form:
( p R + 3 v R 2 ) ( v R − 1 / 3 ) = ( 8 / 3 ) T R {\displaystyle \left(p_{R}+{\frac {3}{v_{R}^{2}}}\right)(v_{R}-1/3)=(8/3)T_{R}}
This equation is invariant for all fluids; that is, the same reduced form equation of state applies, no matter what a and b may be for the particular fluid.
This invariance may also be understood in terms of the principle of corresponding states. If two fluids have the same reduced pressure, reduced volume, and reduced temperature, we say that their states are corresponding. The states of two fluids may be corresponding even if their measured pressure, volume, and temperature are very different. If the two fluids' states are corresponding, they exist in the same regime of the reduced form equation of state. Therefore, they will respond to changes in roughly the same way, even though their measurable physical characteristics may differ significantly.
Cubic equation[edit]
The van der Waals equation is a cubic equation of state; in the reduced formulation the cubic equation is:
v R 3 − 1 3 ( 1 + 8 T R p R ) v R 2 + 3 p R v R − 1 p R = 0 {\displaystyle {v_{R}^{3}}-{\frac {1}{3}}\left({1+{\frac {8T_{R}}{p_{R}}}}\right){v_{R}^{2}}+{\frac {3}{p_{R}}}v_{R}-{\frac {1}{p_{R}}}=0}
At the critical temperature, where T R = p R = 1 {\displaystyle T_{R}=p_{R}=1} we get as expected
v R 3 − 3 v R 2 + 3 v R − 1 = ( v R − 1 ) 3 = 0 ⟺ v R = 1 {\displaystyle {v_{R}^{3}}-3v_{R}^{2}+3v_{R}-1=\left(v_{R}-1\right)^{3}=0\quad \Longleftrightarrow \quad v_{R}=1}
For TR < 1, there are 3 values for vR. For TR > 1, there is 1 real value for vR.
The solution of this equation for the case where there are three separate roots may be found at Maxwell construction
Application to compressible fluids[edit]
The equation is also usable as a PVT equation for compressible fluids (e.g. polymers). In this case specific volume changes are small and it can be written in a simplified form:
( p + A ) ( V − B ) = C T , {\displaystyle (p+A)(V-B)=CT,\,}
where p is the pressure, V is specific volume, T is the temperature and A, B, C are parameters.
See also[edit]
Gas laws
Ideal gas
Inversion temperature
Iteration
Maxwell construction
Real gas
Theorem of corresponding states
van der Waals constants (data page)
References[edit]
^ Jump up to: a b c d Silbey, Robert J.; Alberty, Robert A.; Bawendi, Moungi G. (2004). Physical Chemistry (4th ed.). Wiley. ISBN 978-0471215042.
^ Jump up to: a b c "J. D. Van der Waals, The equation of state for gases and liquids". Nobel Lectures, Physics 1901-1921 (PDF). Amsterdam: Elsevier Publishing Company. 1967. pp. 254–265.
Jump up ^ Andrews, T. (1869). "The Bakerian Lecture: On the Gaseous State of Matter". Philosophical Transactions of the Royal Society of London. 159: 575–590. doi:10.1098/rstl.1869.0021. [non-primary source needed]
Jump up ^ Klein, M. J. (1974). "The Historical Origins of the van der Waals Equation". Physica. 73 (1): 31. Bibcode:1974Phy....73...28K. doi:10.1016/0031-8914(74)90224-9.
Jump up ^ van der Waals; J. D. (1873). Over de Continuiteit van den Gas- en Vloeistoftoestand. University of Leiden.
Jump up ^ Maxwell, J.C. (1874). "Over de Continuïteit van den Gas-en Vloeistof[-]toestand, Academisch Proefschrift". Nature. 10 (259): 477–480. Bibcode:1874Natur..10..477C. doi:10.1038/010477a0. Retrieved 25 June 2015.
Jump up ^ Maxwell, J.C. (1890). "LXIX. Van der Waals on the Continuity of the Gaseous and Liquid States". In Niven, W. D. The scientific papers of James Clerk Maxwell, vol II. Cambridge University Press. pp. 407–415.
Jump up ^ Chang, Raymond (2014). Physical Chemistry for the Chemical Sciences. University Science Books. p. 14. ISBN 978-1-891389-69-6.
Jump up ^ "Deviations from Idal Gas Law Behavior". Purdue University. [self-published source?][better source needed]
^ Jump up to: a b Terrell L. Hill, 2012 [1960], "An Introduction to Statistical Thermodynamics" [Dover Books on Physics], Chicago, IL, USA:R.R. Donnelly (Courier/Dover), ISBN 0486130908, see [1], accessed 25 June 2015. Note, this Donnelly edition is a reprint of the 1986 Dover edition, which itself reprinted the 1962 corrected version of the original 1960 text [Addison Wesley Series in Chemistry, Francis T. Bonner & George C. Pimentel, Eds.], Reading, MS, USA:Addison-Wesley.
Jump up ^ S. I. Sandler, "Chemical and Engineering Thermodynamics," Third Edition. New York: Wiley, 1999, page 273.
Jump up ^ Peter Atkins & Julio de Paula, 2006, "Physical chemistry," 8th Edn., pp. 17-22, 104f, 632-641, New York, NY, USA:Macmillan, ISBN 0716787598, see [2], accessed 21 June 2015.
Jump up ^ R. Stephen Berry, Stuart A. Rice & John Ross, 2000, "Physical Chemistry," pp. 298-306 and passim, Oxford, OXON, ENG:Oxford University Press, ISBN 0195105893, see [3] and [4], accessed 25 June 2015.
Jump up ^ Ken A. Dill & Sarina Bromberg, 2003, "Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology," pp. 457-462, New York, NY, USA:Garland Science, ISBN 0815320515, see [5], accessed 25 June 2015.
Jump up ^ Hill, Terrell L. (1960). An Introduction to Statistical Thermodynamics. Courier Corporation. p. 77.
Jump up ^ Denker, John (2014). "Chapter 26.9, Derivation: Particle in a Box". Modern Thermodynamics. CreateSpace Independent Publishing Platform. ISBN 978-1502530356.
^ Jump up to: a b c Sandler, Stanley I. (2006). Chemical, Biochemical, and Engineering Thermodynamics (4th ed.). New York: John Wiley & Sons. p. 284. ISBN 0-471-66174-0.
Jump up ^ Sandler, Stanley I. (2006). Chemical, Biochemical, and Engineering Thermodynamics (4th ed.). New York: John Wiley & Sons. p. 287. ISBN 0-471-66174-0.
Jump up ^ Clerk-Maxwell, J. (1875). "On the Dynamical Evidence of the Molecular Constitution of Bodies". Nature. 11 (279): 357–359. Bibcode:1875Natur..11..357C. doi:10.1038/011357a0. ISSN 0028-0836.
Jump up ^ Maxwell, J.C. (1890). "LXXI. On the Dynamical Evidence of the Molecular Constitution of Bodies". In Niven, W. D. The scientific papers of James Clerk Maxwell, vol II. Cambridge University Press. pp. 418–438.
Jump up ^ Elhassan, A. E.; Craven, R.J.B.; de Reuck, K. M. (1997). "The area method for pure fluids and an analysis of the two-phase region". Fluid Phase Equilibria (130): 167–187. doi:10.1016/S0378-3812(96)03222-0.
Jump up ^ Michael Gershenson, Date Unknown, "Lecture 16. The van der Waals Gas (Ch. 5)," unpublished course slide set from prior teaching of Physics 351, Thermal Physics (Statistics and Thermodynamics), [6] Rutgers University, Department of Physics and Astronomy, see [7], accessed 25 June 2015. Possibly sourced from Daniel V. Schroeder, 2013, "An Introduction to Thermal Physics," New York, NY, USA:Pearson Education, ISBN 1292026219, see [8], accessed 23 June 2015, or an earlier edition. Lack of certainty of sourcing makes material unverifiable.[self-published source?][better source needed]
Jump up ^ Salzman, W. R. (2004). "Critical Constants of the van der Waals Gas". Chemical Thermodynamics. Arizona State University. Retrieved 2015-07-07.
Further reading[edit]
Terrell L. Hill, 2012 [1960], An Introduction to Statistical Thermodynamics [Dover Books on Physics], pp. 286–289, Chicago, IL, USA:R.R. Donnelly (Courier/Dover), ISBN 0486130908, see [9], accessed 25 June 2015. Note, this Donnelly edition is a reprint of the 1986 Dover edition, which itself reprinted the 1962 corrected version of the original 1960 text [Addison Wesley Series in Chemistry, Francis T. Bonner & George C. Pimentel, Eds.], Reading, MS, USA:Addison-Wesley.
Peter Atkins & Julio de Paula, 2006, Physical chemistry, 8th Edn., pp. 17–22, 104f, 632-641, New York, NY, USA:Macmillan, ISBN 0716787598, see [10], accessed 21 June 2015.
R. Stephen Berry, Stuart A. Rice & John Ross, 2000, Physical Chemistry, pp. 298–306 and passim, Oxford, OXON, ENG:Oxford University Press, ISBN 0195105893, see [11] and [12], accessed 25 June 2015.
Michael Cross, 2004, Lecture 3: First Order Phase Transitions, in Physics 127: Statistical Mechanics (Second Term), Pasadena, CA, USA:Division of Physics, Mathematics, and Astronomy, California Institute of Technology, see [13], accessed 25 June 2015.
Ken A. Dill & Sarina Bromberg, 2003, Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology, pp. 457–462, New York, NY, USA:Garland Science, ISBN 0815320515, see [14], accessed 25 June 2015.
David Chandler, 1987, Introduction to Modern Statistical Mechanics, pp. 287–295, Oxford, Oxon, ENG:Oxford University Press, ISBN 0195042778, see [15], accessed 25 June 2015.
Charles Kittel & Herbert Kroemer, 1980, Thermal Physics, Rev. Edn., pp. 287–295, New York, NY, USA:Macmillan, ISBN 0716710889, see [16], accessed 25 June 2015.
A. Dalgarno & W.D. Davison, 1966, "The calculation of van der Waals interactions," in Advances in Atomic and Molecular Physics, 1, 195.
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Phrases from The Hitchhiker's Guide to the Galaxy
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The Hitchhiker's Guide to the Galaxy is a comic science fiction series created by Douglas Adams that has become popular among fans of the genre(s) and members of the scientific community to illustrate facts about cosmology or philosophy.[citation needed]
Contents
[hide]
1 Answer to the Ultimate Question of Life, the Universe, and Everything (42)
1.1 The number 42
1.2 42 Puzzle
1.3 On the Internet and in software
1.4 Cultural references
2 Don't Panic
3 Knowing where one's towel is
4 Mostly Harmless
5 Not entirely unlike
6 Share and Enjoy
7 So Long, and Thanks for All the Fish
8 See also
9 Notes
10 Further reading
Answer to the Ultimate Question of Life, the Universe, and Everything (42)[edit]
The Answer to the Ultimate Question of Life, The Universe, and Everything.
In the radio series and the first novel, a group of hyper-intelligent pan-dimensional beings demand to learn the Answer to the Ultimate Question of Life, The Universe, and Everything from the supercomputer, Deep Thought, specially built for this purpose. It takes Deep Thought 7½ million years to compute and check the answer, which turns out to be 42. Deep Thought points out that the answer seems meaningless because the beings who instructed it never actually knew what the Question was.[1]
When asked to produce The Ultimate Question, Deep Thought says that it cannot; however, it can help to design an even more powerful computer that can. This new computer will incorporate living beings into the "computational matrix" and will run for ten million years. It is revealed as being the planet Earth, with its pan-dimensional creators assuming the form of white lab mice to observe its running. The process is hindered after eight million years by the unexpected arrival on Earth of the Golgafrinchans and is then ruined completely, five minutes prior to completion, when the Earth is destroyed by the Vogons to make way for a new Hyperspace Bypass. In The Restaurant at the End of the Universe, this is revealed to have been a ruse: the Vogons had been hired to destroy the Earth by a consortium of psychiatrists, led by Gag Halfrunt, who feared for the loss of their careers when the ultimate question became known.[2]
Lacking a real question, the mice decide not to go through the whole thing again and settle for the out-of-thin-air suggestion "How many roads must a man walk down?" from Bob Dylan's song "Blowin' in the Wind".
At the end of the radio series, the television series and the novel The Restaurant at the End of the Universe, Arthur Dent, having escaped the Earth's destruction, potentially has some of the computational matrix in his brain. He attempts to discover The Ultimate Question by extracting it from his brainwave patterns, as abusively[3] suggested by Ford Prefect, when a Scrabble-playing caveman spells out forty two. Arthur pulls random letters from a bag, but only gets the sentence "What do you get if you multiply six by nine?"
"Six by nine. Forty two."
"That's it. That's all there is."
"I always thought something was fundamentally wrong with the universe"[2]
Six times nine is, of course, fifty-four. The answer is deliberately wrong. The program on the "Earth computer" should have run correctly, but the unexpected arrival of the Golgafrinchans on prehistoric Earth caused input errors into the system—computing (because of the garbage in, garbage out rule) the wrong question—the question in Arthur's subconscious being invalid all along.[2]
Quoting Fit the Seventh of the radio series, on Christmas Eve, 1978:
Narrator: There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.
There is another theory mentioned, which states that this has already happened.[4]
Some readers who were trying to find a deeper meaning in the passage soon noticed that 613 × 913 is actually 4213 (as (4 × 13) + 2 = 54, i.e. 54 in decimal is equal to 42 expressed in base 13).[4]:128 When confronted with this, the author claimed that it was a mere coincidence, stating that "I may be a sorry case, but I don't write jokes in base 13."[5]
In Life, the Universe and Everything, Prak, a man who knows all that is true, confirms that 42 is indeed The Answer, and confirms that it is impossible for both The Answer and The Question to be known in the same universe as they will cancel each other out and take the Universe with them—to be replaced by something even more bizarre (as described in the first theory) and that it may have already happened (as described in the second).[6] Though the question is never found, 42 is the table number at which Arthur and his friends sit when they arrive at Milliways at the end of the radio series. Likewise, Mostly Harmless ends when Arthur stops at a street address identified by his cry of, "There, number 42!" and enters the club Beta, owned by Stavro Mueller (Stavromula Beta). Shortly after, the Earth is destroyed in all existing incarnations.
The number 42[edit]
Douglas Adams was asked many times why he chose the number 42. Many theories were proposed, including that 42 is 101010 in binary code, that light refracts through a water surface by 42 degrees to create a rainbow, that light requires 10−42 seconds to cross the diameter of a proton.[7] Adams rejected them all. On 3 November 1993, he gave this answer[8] on alt.fan.douglas-adams:
The answer to this is very simple. It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do' I typed it out. End of story.
Adams described his choice as 'a completely ordinary number, a number not just divisible by two but also six and seven. In fact it's the sort of number that you could without any fear introduce to your parents.'[4]
While 42 was a number with no hidden meaning, Adams explained in more detail in an interview with Iain Johnstone of BBC Radio 4 (recorded in 1998 though never broadcast)[9] to celebrate the first radio broadcast's 20th anniversary. Having decided it should be a number, he tried to think what an "ordinary number" should be. He ruled out non-integers, then he remembered having worked as a "prop-borrower" for John Cleese on his Video Arts training videos. Cleese needed a funny number for the punchline to a sketch involving a bank teller (himself) and a customer (Tim Brooke-Taylor). Adams believed that the number that Cleese came up with was 42 and he decided to use it.[10]
Adams had also written a sketch for The Burkiss Way called "42 Logical Positivism Avenue", broadcast on BBC Radio 4 on 12 January 1977[11] – 14 months before the Hitchhiker's Guide first broadcast "42" in Fit the Fourth, 29 March 1978.[4]
Burkiss Way, "Logical Positivism" sketch excerpt
An excerpt from Douglas Adams' The Burkiss Way sketch, "Logical Positivism" excerpt
Problems playing this file? See media help.
In January 2000, in response to a panelist's "Where does the number 42 come from?" on the radio show "Book Club", Adams explained that he was "on his way to work one morning, whilst still writing the scene, and was thinking about what the actual answer should be. He eventually decided that it should be something that made no sense whatsoever – a number, and a mundane one at that. And that is how he arrived at the number 42, completely at random."
Stephen Fry, a friend of Adams, claims that Adams told him "exactly why 42", and that the reason is "fascinating, extraordinary and, when you think hard about it, completely obvious."[12] However, Fry says that he has vowed not to tell anyone the secret, and that it must go with him to the grave. John Lloyd, Adams' collaborator on The Meaning of Liff and two Hitchhiker's fits, said that Adams has called 42 "the funniest of the two-digit numbers."[13]
The number 42 appears frequently in the work of Lewis Carroll, and some critics have suggested that this was an influence. They note, in particular, that Alice's attempt at her times tables (chapter two of Alice's Adventures in Wonderland) breaks down at 4 x 13 answered in base 42,[14][15] which virtually reverses the failure of 'the Question' ("What do you get if you multiply six by nine?"), in that the latter would equal "42" if calculated in base 13. They find further evidence of Carroll's influence in the fact that Adams entitled the episodes of the original radio series of The Hitchhiker's Guide to the Galaxy "fits", the word Carroll used to name the chapters of The Hunting of the Snark.
There is the persistent tale that 42 is Adams' tribute to the indefatigable paperback book, and is the average number of lines on an average page of an average paperback.[16] Another common guess is that 42 refers to the number of laws in cricket, a recurring theme of the books.[17]
The number 42 also happens to be the ASCII code for the asterisk '*' which is a wildcard character indicating any number of characters or even an empty string in programming. This could be interpreted as the answer 'anything you want it to be'. [18]
42 Puzzle[edit]
The 42 puzzle. The shape of the islands in the background spells out 42, and there are 42 coloured balls
The 42 Puzzle is a game devised by Douglas Adams in 1994 for the United States series of The Hitchhiker's Guide to the Galaxy books. The puzzle is an illustration consisting of 42 multi-coloured balls, in 7 columns and 6 rows. Douglas Adams has said,
Everybody was looking for hidden meanings and puzzles and significances in what I had written (like 'is it significant that 6×9 = 42 in base 13?' As if.) So I thought that just for a change I would actually construct a puzzle and see how many people solved it. Of course, nobody paid it any attention. I think that's terribly significant.[19]
In the puzzle the question is unknown, but the answer is already known to be 42. This is similar to the book where the "Answer to the Ultimate Question of Life, the Universe, and Everything" is known but not the question. The puzzle first appeared in The Illustrated Hitchhiker's Guide to the Galaxy. It was later incorporated into the covers of all five reprinted "Hitchhiker's" novels in the United States.
Adams has described the puzzle as depicting the number 42 in ten different ways. Six possible questions are:[20]
(1) How many spheres are in the diagram? (six rows of seven is 42) (2) What position in the grid does the Earth occupy? (42)
(3) The barcode on one of the spheres is the number 42 as an Interleaved 2 of 5 barcode
(4) Considering red-hued spheres (red, purple, orange, black) as a '1' and those without as a '0', what number does each line represent in decimal form? (In binary, each line reads '0101010', or '42' in decimal form.) (5) What number do the blue-tinted spheres (blue, green, purple, black) spell out? (Similar to a colour blindness test.) (42) (6) What number is represented by Roman numerals spelled out by the yellow-tinted spheres (yellow, orange, green, black) in the first three rows? (XLII = 42)
On the Internet and in software[edit]
The number 42 and the phrase, "Life, the universe, and everything" have attained cult status on the Internet. "Life, the universe, and everything" is a common name for the off-topic section of an Internet forum and the phrase is invoked in similar ways to mean "anything at all". Many chatbots, when asked about the meaning of life, will answer "42". Several online calculators are also programmed with the Question. Google Calculator will give the result to the answer to life the universe and everything as 42, as will Wolfram's Computational Knowledge Engine.[21] Similarly, DuckDuckGo also gives the result of the answer to the ultimate question of life, the universe and everything as 42.[22] In the online community Second Life, there is a section on a sim called "42nd Life." It is devoted to this concept in the book series, and several attempts at recreating Milliways, the Restaurant at the End of the Universe, were made.
In OpenOffice.org software (prior to version 3.4) if =ANTWORT("Das Leben, das Universum und der ganze Rest") (German for =ANSWER("life, the universe and everything")) is typed into any cell of a spreadsheet, the result is 42.[23]
ISO/IEC 14519-2001/ IEEE Std 1003.5-1999, IEEE Standard for Information Technology – POSIX(R) Ada Language Interfaces – Part 1: Binding for System Application Program Interface (API) , uses the number 42 as the required return value from a process that terminates due to an unhandled exception. The Rationale says "the choice of the value 42 is arbitrary" and cites the Adams book as the source of the value.
The random seed chosen to procedurally create the whole universe of the online multi-player computer game EVE Online was chosen as 42 by its lead game designer in 2002.[24]
In the computer game Gothic "42" is a code that deactivates all activated cheats. After typing "42" in a right place, text "What was the question?" appears.
The OpenSUSE team decided the next version will be based on SUSE Linux Enterprise Desktop and named "Leap 42". The number 42 was chosen as a reference to the answer to life, the universe and everything.[25]
Cultural references[edit]
The Allen Telescope Array, a radio telescope used by SETI, has 42 dishes in homage to the Answer.[26]
In the American TV show Lost, 42 is the last of the mysterious numbers 4, 8, 15, 16, 23, and 42. In an interview with Lostpedia, producer David Fury confirmed this was a reference to Hitchhiker's.[27]
The British TV show The Kumars at No. 42 is so named because show creator Sanjeev Bhaskar is a Hitchhiker's fan.[28]
The band Coldplay's album Viva la Vida includes a song called "42". When asked by Q magazine if the song's title was Hitchhiker's-related, Chris Martin said, "It is and it isn't."[29]
The band Level 42 chose its name in reference to the book.[30]
The episode "42" of the British science fiction television series Doctor Who was named in reference to the Answer. Writer Chris Chibnall acknowledged that "it's a playful title".[31]
Ken Jennings, defeated along with Brad Rutter in a Jeopardy! match against IBM's Watson, writes that Watson's avatar which appeared on-screen for those games showed 42 "threads of thought," shown as colorful lines spinning around Watson's logo, and that the number was chosen in reference to this meme.[32]
The Hitchhiker knitting pattern, designed by Martina Behm, is a scarf with 42 teeth.[33]
In The Flash, Season 4, Episode 1, Cisco in trying to decipher what Barry is writing explicitly says that what Barry says might solve answer to the Life, the Universe and Everything, which Caitlin suggests is 42. [34]
In The X-Files, Fox Mulder lives in apartment 42. This has been acknowledged by the show's creator, Chris Carter, as a reference to Hitchhikers[35]
Don't Panic[edit]
Towels in Innsbruck with the words "DON'T PANIC" on Towel Day
In the series, Don't Panic is a phrase on the cover of The Hitchhiker's Guide to the Galaxy.[1] The novel explains that this was partly because the device "looked insanely complicated" to operate, and partly to keep intergalactic travellers from panicking.[36] "It is said that despite its many glaring (and occasionally fatal) inaccuracies, the Hitchhiker's Guide to the Galaxy itself has outsold the Encyclopedia Galactica because it is slightly cheaper, and because it has the words 'DON'T PANIC' in large, friendly letters on the cover."[1]
Arthur C. Clarke said Douglas Adams' use of "don't panic" was perhaps the best advice that could be given to humanity.[37]
Knowing where one's towel is[edit]
Somebody who can stay in control of virtually any situation is somebody who is said to know where his or her towel is. The logic behind this statement is presented in chapter 3 of The Hitchhiker's Guide to the Galaxy thus:
... a towel has immense psychological value. For some reason, if a strag (strag: nonhitchhiker) discovers that a hitchhiker has his towel with him, he will automatically assume that he is also in possession of a toothbrush, washcloth, soap, tin of biscuits, flask, compass, map, ball of string, gnat spray, wet-weather gear, space suit etc., etc. Furthermore, the strag will then happily lend the hitchhiker any of these or a dozen other items that the hitchhiker might accidentally have "lost". What the strag will think is that any man who can hitch the length and breadth of the galaxy, rough it, slum it, struggle against terrible odds, win through, and still knows where his towel is, is clearly a man to be reckoned with.
Adams got the idea for this phrase when he went travelling and found that his beach towel kept disappearing. In 'The Hitchhiker's Guide to the Galaxy -The Radio Scripts', his friends describe how he would always "mislay" his towel. On Towel Day, fans commemorate Adams by carrying towels with them.
Mostly Harmless[edit]
The only entry about Earth in the Guide used to be "Harmless", but Ford Prefect managed to change it a little before getting stuck on Earth. "Mostly Harmless" provoked a very upset reaction from Arthur when heard. (Those two words are not what Ford submitted as a result of his research—merely all that was left after his editors were done with it.) It is the title of the fifth book in the Hitchhiker series. Its popularity is such that it has become the definition of Earth in many standard works of sci-fi reference, like The Star Trek Encyclopedia. Additionally, "Harmless" and "Mostly Harmless" both feature as ranks in the computer game Elite. Also, in World of Warcraft, there is a rifle that fires (mostly) harmless pellets.[38] In the MMORPG RuneScape, there is an island called Mos Le Harmless (Mostly Harmless). Low-scoring players in the multiplayer version of the game Perfect Dark and GoldenEye 007 are awarded with the designation "mostly harmless". In the 2008 edition of the board game Cosmic Encounter, the Human race is given the attribute "Mostly Harmless". In the game Kerbal space program, there is an atomic rocket motor with the description "mostly harmless".
Not entirely unlike[edit]
In the novel The Restaurant at the End of the Universe, Arthur Dent tries to get a Nutrimatic drinks dispenser to produce a cup of tea. Instead, it invariably produces a concoction (which most people found unpleasant) that is "almost, but not quite, entirely unlike tea". One of the primary goals of the player, as Arthur Dent, in the computer game The Hitchhiker's Guide to the Galaxy, is to thwart the machine and find some decent tea, a mission that the player is constantly reminded of by the inventory item "no tea". According to the Jargon File, the briefer "not entirely unlike" has entered hacker jargon.[39]
Share and Enjoy[edit]
"Share and Enjoy" is the slogan of the Sirius Cybernetics Corporation Complaints Division. In the radio version, this phrase had its own song (sung in Fit the Ninth of the radio series), which was sung by a choir of robots during "special occasions". The Sirius Cybernetics Corporation tends to produce inherently faulty goods, which renders the statement ironic since few people would want to "Share and Enjoy" something that was defective. Among the design flaws is the choir of robots that perform this song: they sing a tritone out of tune with the accompaniment. The Guide relates that the words "Share and Enjoy" were displayed in illuminated letters three miles high near the Sirius Cybernetics Complaints Division, until their weight caused them to collapse through the underground offices of many young executives. The upper half of the sign that now protrudes translates in the local tongue as "Go stick your head in a pig", and is lit up only for special celebrations.
The episode Fit the Twentieth of the radio series features a personal computer OS booting sound (à la The Microsoft Sound) set to the tune of "Share and Enjoy". Furthermore, Fit the Twenty-First of the radio series, the last episode in the adaptation of the novel So Long, and Thanks for All the Fish, features a polyphonic ringtone version of the tune. The "Share and Enjoy" tune also is used in the TV series as the backing for a Sirius Cybernetics Corporation robot commercial (slogan: "Your plastic pal who's fun to be with!").
So Long, and Thanks for All the Fish[edit]
After mice, the second most intelligent species on Earth were the dolphins.
The dolphins had long known of the impending demolition of Earth and had made many attempts to alert mankind to the danger...The last ever dolphins message was misinterpreted as a surprisingly sophisticated attempt to do a double backward somersault through a hoop whilst whistling "The Star-Spangled Banner," but in fact the message was this: "So Long, and Thanks for All the Fish."
—  Douglas Adams, The Hitchhiker's Guide to the Galaxy
The line was also the title of the fourth book in the trilogy, and appears in that book as a message inscribed on crystal bowls left as parting gifts from the dolphins to the human race. Its popularity was such that it was the title of the opening song for the 2005 movie The Hitchhiker's Guide to the Galaxy.
The phrase was spoofed for the NOFX album So Long, and Thanks for All the Shoes.[citation needed]
The phrase was also spoofed for the All Time Low track "So Long, and Thanks for All the Booze", from the appropriately-titled album Don't Panic.[citation needed]
When the air traffic control unit at Perth Airport (ICAO code: EGPT) in Scotland was closed following a downturn in commercial pilot training, for which the airport was best known, the final NOTAM (notice to airmen) issued by the unit via the AFTN stated, "This is Perth ATC signing off. So long and thanks for all the fish."[citation needed]
See also[edit]
Wikiquote has quotations related to: The Hitchhiker's Guide to the Galaxy
42 (number)
Apophenia
Meaning of life
Somebody Else's Problem
Notes[edit]
^ Jump up to: a b c Adams, Douglas (1979). The Hitchhiker's Guide to the Galaxy. Pocket Books. p. 3. ISBN 0-671-46149-4.
^ Jump up to: a b c Douglas Adams (1 January 1980). The Restaurant at the End of the Universe. ISBN 0-345-39181-0.
Jump up ^ episode 6 of the TV series
^ Jump up to: a b c d The Original Hitchhiker Radio Scripts. Douglas Adams, edited by Geoffrey Perkins. Pan Books, London. 1985. ISBN 0-330-29288-9
Jump up ^ Diaz, Jesus. "Today Is 101010: The Ultimate Answer to the Ultimate Question". io9. Retrieved 2017-05-08.
Jump up ^ Douglas Adams (1982). Life, the Universe and Everything. ISBN 0-330-26738-8.
Jump up ^ Peter Minearo, Mike Smith (3 April 2007). "In Hitchhiker's Guide to the Galaxy, 42 is the number from which all meaning could be derived". CIO (chief information officer) Magazine. Retrieved 3 March 2008.
Jump up ^ "Why 42 ? – alt.fan.douglas-adams – Google Groups". Retrieved 1 September 2007.
Jump up ^ This interview is contained on Douglas Adams's Guide to The Hitch-Hiker's Guide to the Galaxy (BBC Cassette ISBN 0-563-55236-0) and The Hitchhiker's Guide to the Galaxy – The Collectors Edition (BBC CD ISBN 0-563-47702-4)
Jump up ^ Several attempts by fans to find this particular video have been unsuccessful and it is possible it may never have been published or has since been deleted from use.
Jump up ^ This is found on the Douglas Adams at the BBC CD set (ISBN 0-563-49404-2)
Jump up ^ "BBC News – Magazine – What on earth is 42?". 7 March 2008. Retrieved 22 March 2008.
Jump up ^ John Lloyd speaking at the 30th Anniversary Hitchhiker's recording at Douglas Adams Memorial Lecture on Wednesday 12 March 2008 at The Royal Geographical Society
Jump up ^ Lewis Carroll and Douglas Adams.
Jump up ^ The Mystery of Lewis Carroll, Jenny Woolf
Jump up ^ Vernon, Mark (7 March 2008). "What on earth is 42?". BBC News. Retrieved 9 June 2008.
Jump up ^ Douglas Adams and the cult of 42 | Books. The Guardian (2013-09-03). Retrieved on 2013-09-07.
Jump up ^ http://ascii.cl/
Jump up ^ "Cool questions and answers with Douglas Adams". Archived from the original on 23 May 2007. Retrieved 19 August 2007.
Jump up ^ "4.8 Probable Solution to the Ill Guide Puzzle (Douglas Adams)". Retrieved 19 August 2007.
Jump up ^ "answer to life, the universe, and everything – Wolfram|Alpha". Wolframalpha.com. Retrieved 26 July 2011.
Jump up ^ "the answer to the ultimate question of life, the universe and everything at Duck Duck Go". Duckduckgo.com. 10 October 2010. Retrieved 26 July 2011.
Jump up ^ "Easter Eggs – OpenOffice.org Wiki". Wiki.services.openoffice.org. 21 April 2010. Retrieved 26 July 2011.
Jump up ^ Emilsson, Kjartan (Speaker) (23 March 2012). DUST 514 Seeding The Universe (Television production). Iceland: CCP Games.
Jump up ^ "openSUSE Leap 42 Is a New Version That Will Change the openSUSE Project". http://news.softpedia.com/. 7 July 2015. Retrieved 23 September 2015. External link in |publisher= (help)
Jump up ^ Jacqui Hayes (2010). "Silent witness". Cosmos. Archived from the original on 5 April 2012. Retrieved 20 August 2010.
Jump up ^ "Lostpedia interview with David Fury". Lostpedia.wikia.com. 20 May 2008. Retrieved 26 July 2011.
Jump up ^ "10 things we didn't know this time last week". BBC News. 14 November 2003. Retrieved 17 February 2009.
Jump up ^ "Coldplay: Viva La Vida". Q magazine. Archived from the original on 15 July 2009. Retrieved 9 March 2009.
Jump up ^ Mandy Carter (2006). "Interview: Mark King – Level 42". Official site: Level 42. Archived from the original on 7 September 2012. Retrieved 4 April 2009.
Jump up ^ Darlington, David (April 2007). "Script Doctors: Chris Chibnall". Doctor Who Magazine (381): 24–30.
Jump up ^ Ken Jennings (16 February 2011). "My Puny Human Brain". Slate magazine.
Jump up ^ Martina Behm (2010). "Hitchhiker". Ravelry. Retrieved 5 June 2015.
Jump up ^ imdb. http://www.imdb.com/title/tt6403450/. Missing or empty |title= (help)
Jump up ^ The Complete X-Files: Behind the Scenes, the Myths, and the Movies
Jump up ^ Adams, Douglas (1979). The Hitchhiker's Guide to the Galaxy. Pocket Books. p. 27. ISBN 0-671-46149-4.
Jump up ^ Zebrowski, George (30 June 2008). "Arthur C. Clarke looks back on the lifetime of influences that led him to become a science-fiction Grand Master". Sci Fi Weekly. SCI FI. Archived from the original on 23 July 2008. Retrieved 24 July 2008. The best advice I think was given by Douglas Adams: "Don't panic."
Jump up ^ http://www.wowhead.com/item=46725/red-rider-air-rifle
Jump up ^ "not entirely unlike X" – The Jargon File (version 4.4.7)
Further reading[edit]
Smith, Mol (2007). 42 – The Answer to Life, The Universe, and Everything. Maurice Smith. pp. 178 pages. ISBN 978-0-9557137-0-5.
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