Calculating Entropy Change of Ideal Gas

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SUMMARY

The discussion focuses on calculating the entropy change of 3 moles of an ideal gas during isothermal compression from a volume of 5V to V at a temperature of 30°C. The correct approach involves recognizing that for an isothermal process, the internal energy change (dU) is zero, and the relationship PV = nRT applies. The user is guided to derive the expression for the change in entropy (dS) using the formula S = W/T, where W is the work done during the compression, and to integrate the resulting expression to find the total change in entropy.

PREREQUISITES
  • Understanding of ideal gas laws, specifically PV = nRT
  • Knowledge of thermodynamic processes, particularly isothermal and adiabatic processes
  • Familiarity with the concepts of entropy and internal energy
  • Ability to perform calculus, particularly integration
NEXT STEPS
  • Study the derivation of the entropy change formula for isothermal processes
  • Learn about the first law of thermodynamics and its application to ideal gases
  • Explore the differences between isothermal and adiabatic processes in thermodynamics
  • Practice problems involving the calculation of work done in isothermal processes
USEFUL FOR

Students studying thermodynamics, particularly those preparing for exams in physics or engineering, as well as educators looking for clear explanations of entropy changes in ideal gases.

Brewer
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I have found the following question on a previous exam paper whilst I've been doing my revision, and have a few questions about how to set up my answer.

Question:
Calculate the entropy change of 3 moles of an ideal gas when they are isothermally compressed (T = 30° C) from a volume 5V to a volume V.

My initial thought was to use PV = nRT, but because both n and T stay constant I then started thinking that I could just make P1V1 = P2V2.

However from my notes I have that PV^gamma = constant which confused me as there is no mention of a value for gamma in the question.

From here I would use the formula W=-integralP(V)dV and then use the S=W/T formula.

Is this the correct way to go with this question?

Thanks for any feedback
 
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It's simpler than that. Try to answer the following questions in order.

1.) For an isothermal process, what is dU?
2.) Can you find an expression for dU in terms of dS and dV? (since after all you were given 2 volumes and you were asked for the change in entropy).
3.) Can you integrate the expression found in 2.)?

That should get you there.
 
PV^1 = constant for an isothermal process (treating it as an ideal gas ...)
PV^gamma = constant for an adiabatic process.
 

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