(24 points) To calculate the multiplicity for a classical model ofideal gasowe c

Question

(24 points) To calculate the multiplicity for a classical model ofideal gasowe can count the ways to allocate total energy Uamong N molecules in the form of kinetic energy (e 2m, where p is the momentum and m is the mass of the molecule) and the total number of ways to position these N molecules in a volume V. The procedure leads to the following expression: (U ,V,N) = const VNU3N/2 Determine: a) equation of state for ideal gas in this case; b) internal energy of ideal gas as a function of temperature and its heat capacity; c) entropy change when the temperature is increased form T, to T2.

Explanation / Answer

E = 1/2 m v2

2 E = m v2

2 E m = m2 v2

2 E m = P2

where P = m v

so

P = ( 2 m E )1/2

or

E = P2 / 2 m

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