How to Calculate Entropy of an Ideal Gas During Expansion?

AI Thread Summary
To calculate the entropy change of an ideal gas during expansion, the equation ΔS = nRln(Vf/Vi) + nCv,m ln(Tf/Ti) is used, where n is the number of moles, R is the gas constant, and Cv,m is the molar heat capacity. The initial and final conditions include n = 1 mol, Cv,m = 1.5R, Ti = 300K, and Tf = 200K, with the gas expanding against an external pressure of Pext = 1 bar to double its volume. Pressure does not need to be explicitly included in the calculations, as it is accounted for in the p-v-T relationships of the ideal gas. The focus should be on the volume and temperature ratios when applying the entropy change equation. Understanding these relationships allows for accurate entropy calculations without needing to directly incorporate pressures.
ChristineMarie
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How do you calculate the entropy of an ideal gas with n = 1, Cv,m = 1.5R, Ti = 300K, P=3bar and expands against Pext = 1bar until final volume is twice initial volume at Tf = 200K?
 
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ChristineMarie said:
How do you calculate the entropy of an ideal gas with n = 1, Cv,m = 1.5R, Ti = 300K, P=3bar and expands against Pext = 1bar until final volume is twice initial volume at Tf = 200K?
What equations do you know that relate to entropy? How does this relate to the heat capacity? Also, you've left most of your units off!
 
ΔS = nRln(Vf/Vi) + nCv,mln(Tf/Ti).
Only the mole unit, n = 1mol?
R is a constant = 8.3145J/mol.K = 0.083145L.bar/mol.K
 
I'm just not sure how to incorporate the pressures, if I even need to. But if I don't need to use the pressures I would like to understand why.
 
ChristineMarie said:
I'm just not sure how to incorporate the pressures, if I even need to. But if I don't need to use the pressures I would like to understand why.
To get the entropy change from the initial equilibrium state to the final equilibrium state of a system, you need to dream up a reversible path between these two states, and then evaluate the integral of dq/T for that path. In the case of an ideal gas, you also need to take into account the p-v-T relationship for the gas. The equation you wrote down takes all this into consideration, and has done all the work for you. So all you need to do is to substitute the volume ratio and temperature ratio in. The pressure is already implicitly taken into consideration by the equation.

Chet
 
Thank you!
 
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