Scientia Sinica

36 SCIENTIA SINICA Vol, V

and internal degrees of freedom (hereafter referred to as external state and internal state respectively), and thus talk about external temperature Te and internal temperature JT“ and also external heat capacity C®, internal heat capacity C™, and total heat capacity C=C°+C. During compression by the application of a constant pressure, the mechanical energy will first turn into thermal energy associated with the external degrees of freedom, so that obviously we shall have T°>T, and T™ tends to decrease while TO tends to increase so that s < 50, inasmuch as the volume depends solely on the external degrees of freedom. When thermodynamic equilibrium is attained, 7? = =T° and s=s9. When the applied pressure is withdrawn, so= 0, the thermal energy associated with the external degrees of freedom will first turn into mechanical energy so that T?<T™, T tends to increase while JT“ tends to decrease, and therefore s > 59. Hence) to a first approximation, one may expect to have s)—s proportional to fO = T®. Furthermore, since upon compression s —s. is caused by the transfer of the thermal energy from external into internal degrees of freedom, we may likewise expect to have d(s—s.) proportional to dT, i.e., we may have

Sess TOT aml d(s—sa) me dT T2 T dt dt

Thus, our equation of volume irreversibility (4) is seen to imply in this case

aT) TATE) a a

with T,,= constant X T,. Equation (10) is just the equation of thermal irreversibility that was assumed by Herzfeld and Rice. Starting with this equation and noting that pressure is due to translational motion alone so that T® and V determine the pressure, p=p(T™, V), of the non-equilibrium state in exactly the same way as T and V determine the pressure of the state of thermodynamic equilibrium, one can, by means of thermodynamic relations, arrive at an equation for the change of non-equilibrium states that is formally identical with our visco-elastic equation (9). For instance, this derivation has been comprehensively given in the review article by Markham, Beyer and Lindsay"! (equation (6.14) ). Comparing the two equations, the thermal relaxation time is seen to be

Tih =e T2. (11) Gs

In molecular theories, 7,, is, for a gas almost completely unexcited, the mean lifetime of the excited internal state responsible for the relaxation, being the reciprocal of the probability per molecule per unit time of the transition in question!”!,