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Cv is constant volume, which is times the constant R. You use this in deltaS=nCvln(t2/t1) instead of deltaS=nRln(V2/v1) when you have a monatomic ideal gas at constant volume to calculate for entropy.
If the problem gives you temperature and the system is not isothermal, deltaS=nCvln(t2/t1) is used to determine the change in entropy. To calculate the change in entropy of an ideal gas in a reversible isothermal expansion, use deltaS=nRln(V2/V1).
Emily Kennedy 4L wrote:where does the 3/2 come from?
For heat capacities of ideal gases, we use Cv=3/2R for a monoatomic gas and Cv=5/2R for a diatomic gas such as N2 or H2. The constant being multiplied to R is determined by the greater number of degrees of freedom in diatomic as opposed to monoatomic gases, so 5/2 (diatomic) is much bigger than 3/2 (monoatomic).
If a gas is compressed suddenly and irreversibly, treat it as a two step process where the dS from dT and dS from dV need to be accounted for. In this case, you would do dS=nCvln(T2/T1) if v was constant + deltaS=nRln(V2/V1).
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