Cp and Cv Values

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

Mia Navarro 1D
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Joined: Fri Sep 29, 2017 7:04 am

Cp and Cv Values

Why does the Cp value use the 5/2 fraction, but Cv use the 3/2 fraction? I know one is the derivative of the other but I’m not sure how that process works?

Dylan Davisson 2B
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Re: Cp and Cv Values

In regards to the two types of molar heat capacities of an ideal gas (Cp and Cv), both are related by the equation Cp= Cv + R. This relationship is derived from the equation deltaH = deltaU +nRdeltaT , as shown on page 280 in the textbook. Because the molar heat capacity at a constant volume (Cv) for an atom is equal to (3/2)R, by the equation Cp= Cv + R, the molar heat capacity at a constant pressure (Cp) for an atom would be equal to (5/2)R.

Chem_Mod
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Re: Cp and Cv Values

A monatomic ideal gas has 3 degrees of freedom and each contributes (1/2)nRT towards the internal energy. So the total internal energy would be (3/2)nR. And since equating both we get Cv = 3/2R.

Because Cp-Cv = R, Cp = Cv + R = (5/2)R.

The above post is accurate!