Partition Function Homework: Find Entropy Change for Isothermal Expansion

[senan]

Homework Statement

One mole of a gas obeys the equation of state
(P +a/V² )(1 −b/V) =RT/V
Find the change in entropy if one mole of the gas is isothermally expanded until the volume
is doubled. Express your answer in terms of the initial volume of the gas Vi.

Homework Equations

S₂-S₁=1/T Integral from V_i to 2V_i of PdV

The Attempt at a Solution

I replaced P with P=NkT/V

that leads to

S₂-S₁=-kln(2V_i/V_i)

as the answer was asked for in terms of V_i I'm not sure that's rightsorry titled the question wrong meant to title other Q as partition function

 

[G01]

That is not right.

You are using the wrong equation of state.

It is stated in problem that the gas obeys a different equation of state, not the usual, PV=NkT.

You have to use the given equation of state to express P in terms of V.

 

[ideasrule]

By the way, that equation of state is called the van der Waals equation. It takes into account intermolecular forces and the volume of molecules instead of assuming an ideal gas.