- #1
senan
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Homework Statement
The partition function for a perfect gas containing N monatomic particles of mass m at a
temperature T is
Z =(1/N!)*VN[2(Pi)mkT/h2]3N/2
(2a) Use this partition function to find the molar Helmholtz free energy, molar internal
energy and molar heat capacity at constant volume of the gas.
(2b) Show that the molar entropy of the gas is given by
S = R[lnV/NA+(3/2)ln T +5/2+(3/2)ln(2(Pi)mk/h2)]
and find a simple, general expression for the change in entropy as a function of the temperatures and volumes of the initial and final states.
(2c) Show that this expression for the entropy of the gas is consistent with the expected
change in entropy for (i) an isothermal expansion of one mole of gas from volume V1 to
volume V2 and (ii) heating of one mole of gas from temperature T1 to temperature T2 at
constant volume.
P
Homework Equations
F=-kTlnZ
Cv=(dQ/dT)v
Cv=(dE/dT)v
E=-(dlnZ/dβ) with β=kT
The Attempt at a Solution
I got the helmholtz free energy using the F=-kTlnZ formula. I tried to get the Cv by getting E and then getting (dE/dT)v but the equation is very messy and long and I'm not sure its right. Is E the molar internal energy or do I need another formula.
I havn't really attempted the next two parts but help for part 1 would be appreacited thanks