Change in Entropy for Isothermal Compression of Ideal Gas

[LivvyS]

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 log_e (P₂ / P₁) + Cp log_e (V₂ / V₁)

S₂-S₁ = Cv log_e ((P₂V₂^γ) / (P₁V₁^γ))

PV=nRTAttempt at answer:
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.

Thanks in advance for your help guys!

 

[Chestermiller]

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

Chet

 

[LivvyS]

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

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

 

[Chestermiller]

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

Im not even 100% certain that I am approaching this question correctly, I feel as though I've hit a bit of a wall with it.

$C_p/C_v=\gamma$

$C_p-C_v=R$

Two equations, two unknowns.

Chet

 

[Chestermiller]

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

Chet

 

[LivvyS]

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]

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