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Molar specific heat at constant volume for an ideal gas (15-18)

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Molar specific heat of an ideal gas at constant pressure

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Review

We'll user the symbol D to represent the number of degrees of freedom. Then the average energy per gas molecule is (D/2)kT. One mole of the gas contains Avogadro's number of molecules, so the energy per mole is NA(D/2)kT=(D/2)(NAk)T=(D/2)RT (Again, recall that k=R/NA, so R=NAk.) Then the internal energy of n moles of ideal gas is

(15-16)     U=n(D2R)T  (ideal gas, D degrees of freedom)

If the temperature of the gas changes by ΔT, it follows from Equation 16-16 that the internal energy change is

(15-17)  ΔU=n(D2R)ΔT  (ideal gas, D degrees of freedom)

But we saw above that for an ideal gas, ΔU=nCVΔT. Comparing this to Equation 15-17, we see that