Calculating Entropy Change of Ideal Gas

[Brewer]

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 forumla 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

 

[quantumdude]

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.

 

[lightgrav]

PV^1 = constant for an isothermal process (treating it as an ideal gas ...)
PV^gamma = constant for an adiabatic process.