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# hwk10 - T 1 and container 2 at T 2 6 = T 1 Using the...

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PH421 - Thermal and Statistical Physics Assignment 10 - Mar 12, 2008 1. Equation of state and energy of an ideal gas An ideal gas enclosed in a volume V is composed of N identical particles in equilibrium at temperature T . (a) Write down the N -particle classical partition function Z in terms of the single-particle partition function ζ , and show that Z it can be written as ln ( Z ) = N ln V N + 3 2 ln ( T ) + σ (1) where σ does not depend on either N , T or V . (b) From Equation 1 derive the mean energy E , the equation of state of the ideal gas and C V . 2. Temperature equalization in an ideal gas Consider two containers of same volume V , each containing the same number ν of moles of an ideal gas; container # 1 is at
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Unformatted text preview: T 1 and container # 2 at T 2 6 = T 1 . Using the entropy of an ideal gas derived from the classical partition function, show that the temperature equalization process is irreversible . You may consider that equalization is achieved by placing the two containers in contact with each other via a partition that has no heat capacity, i.e., the gases can exchange heat between themselves, but not to the partition or the walls of the container. (Notice that this result was earlier derived based on pure thermodynamical arguments). 3. Problem 7.4 from the textbook....
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