. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. FUNDAMENTAL EQUATIONS OF IDEAL GASES 381 In general the heat capacities are known over a Hmited range of temperature, for H2 is the only gas whose heat capacity is known at low temperatures. The question of whether the heat capacity approaches 3/2 R or vanishes at zero Kelvin is, moreover, not yet settled. In the case of water vapor values of C3 are available to temperatures where water vapor is detectably dissociated. Such values must, however, be corrected for heat absorb
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. FUNDAMENTAL EQUATIONS OF IDEAL GASES 381 In general the heat capacities are known over a Hmited range of temperature, for H2 is the only gas whose heat capacity is known at low temperatures. The question of whether the heat capacity approaches 3/2 R or vanishes at zero Kelvin is, moreover, not yet settled. In the case of water vapor values of C3 are available to temperatures where water vapor is detectably dissociated. Such values must, however, be corrected for heat absorbed due to dissociation; a correction evidently impossible to obtain until the dissociation data can be correlated, and then a final and exact result is only possible by successive approxima- tion. Above zero degrees the heat capacities of most gases increase rather slowly, and in the absence of a generally appli- cable theory of heat capacities of gases linear expressions, or at most quadratic expansions, may be used. On this basis the heat capacity terms become, when the linear form is used, 2^1 / c,*dt = ^v,a, {t - to) + SV (^' - ^0')' (116) J to 2)"! / ci*dt/t = ^via,\og{t/to) + ^vA (t - to). (117) J to The present custom is often to integrate the linear terms between zero Kelvin and t, but such practice, as is frequently the case, had its origin in the earlier erroneous belief that the heat capacity dependence on temperature was as simple below the ice point as it appeared to be above. Note should be taken also of Gibbs' decision to express the reaction pressure- temperature function in terms of the energy constant £"1, a choice very likely induced by the somewhat simpler treatment possible when non-ideal gases are involved. When Zi'i vanishes in (114) [309] the mol fraction function Si'i log xi becomes a function of temperature alone, and thus pressure is without influence on the numbers of the different kinds of molecules so long as the gases are ideal. A furth
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