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Entropy change in gas

  • Thread starter LivvyS
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  • #1
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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


Attempt 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!
 

Answers and Replies

  • #2
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How are Cp and Cv related to R (the ideal gas constant)?

Chet
 
  • #3
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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:
  • #4
19,916
4,093
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
 
  • #5
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Incidentally, for a constant temperature process, what is the equation for the change in entropy as a function of the volume ratio?

Chet
 
  • #6
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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))?
 
  • #7
19,916
4,093
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
 

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