Entropy change in gas

• LivvyS
In summary, the problem involves a sample of nitrogen gas being compressed isothermally to half its original volume. The gas behaves like an ideal gas and the change in entropy can be calculated using the equation S2-S1 = Cv loge (P2 / P1) + Cp loge (V2 / V1). To solve for Cv, the equations C_p/C_v = γ and C_p-C_v = R can be used. Another equation for the change in entropy is ΔS=nR\ln(V_2/V_1).

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 loge (P2 / P1) + Cp loge (V2 / V1)

S2-S1 = Cv loge ((P2V2γ) / (P1V1γ))

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.

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 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?

Last edited:
LivvyS said:
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

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))?

LivvyS said:
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

1. What is entropy change in gas?

Entropy change in gas refers to the measurement of disorder or randomness in a gas system. It is a thermodynamic property that describes the degree of chaos or unpredictability in the particles of a gas.

2. How is entropy change in gas calculated?

The entropy change in gas can be calculated using the formula ΔS = nR ln(V2/V1), where ΔS is the change in entropy, n is the number of moles of gas, R is the gas constant, and V1 and V2 are the initial and final volumes of the gas.

3. What factors affect the entropy change in gas?

The entropy change in gas is affected by several factors, including temperature, pressure, and volume. An increase in temperature or volume leads to an increase in entropy, while an increase in pressure decreases entropy.

4. Why is entropy change in gas important?

Entropy change in gas is an important concept in thermodynamics as it helps to understand the behavior of gases and their energy transformations. It is also used in various industrial processes, such as refrigeration and power generation.

5. Can entropy change in gas be negative?

Yes, entropy change in gas can be negative. This occurs when the gas system becomes more ordered, such as in a compression process. However, the overall change in entropy of the universe must always be positive, in accordance with the second law of thermodynamics.

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