# Entropy change in gas

Problem statement:
A sample of 8.02 × 10-1 moles of nitrogen gas ( γ = 1.40) occupies a volume of 2.00 × 10-2 m3at a pressure of 1.00 × 105 Pa and temperature of 300 K. It is isothermally compressed to half its original volume. It behaves like an ideal gas. Find the change in entropy of the gas.

Relevant equations:

S2-S1 = Cv loge (P2 / P1) + Cp loge (V2 / V1)

S2-S1 = Cv loge ((P2V2γ) / (P1V1γ))

PV=nRT

V2 = 1.00 x 10-2 m3

P2 can be found by P = nRT / V = 2.00 x 105 Pa

I assume Cv must be worked out from γ somehow, but I cannot see how to do this.

Chestermiller
Mentor
How are Cp and Cv related to R (the ideal gas constant)?

Chet

Cp=Cv+nR surely Cp is needed in order to find Cv?

Im not even 100% certain that Im approaching this question correctly, I feel as though ive hit a bit of a wall with it. Perhaps I am trying to use the wrong formula?

Last edited:
Chestermiller
Mentor
Cp=Cv+nR surely Cp is needed in order to find Cv?

Im not even 100% certain that Im approaching this question correctly, I feel as though ive hit a bit of a wall with it.
##C_p/C_v=\gamma##

##C_p-C_v=R##

Two equations, two unknowns.

Chet

Chestermiller
Mentor
Incidentally, for a constant temperature process, what is the equation for the change in entropy as a function of the volume ratio?

Chet

Oh I see, so you then end up with Cv= R/ γ-1. Very helpful, thanks!
Do you mean S2-S1 = Cv loge ((P2V2γ) / (P1V1γ))?

Chestermiller
Mentor
Oh I see, so you then end up with Cv= R/ γ-1. Very helpful, thanks!
Do you mean S2-S1 = Cv loge ((P2V2γ) / (P1V1γ))?
No, I mean ##ΔS=nR\ln(V_2/V_1)##

Chet