The ratio of the specific heats CpCv=γ in terms of degrees of freedom (n) is given by

For n degrees of freedom, Cv=n2R Also, Cp-Cv=RCp=Cv+R=n2R+RCp=n2+1Rγ=CpCv=n2+1R(n/2)R=n+2n ∴ γ=1+2n

The ratio of the specific heats CpCv=γ in terms of degrees of freedom (n) is given by

For n degrees of freedom, Cv=n2R Also, Cp-Cv=RCp=Cv+R=n2R+RCp=n2+1Rγ=CpCv=n2+1R(n/2)R=n+2n ∴ γ=1+2n

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The ratio of the specific heats $\frac{C_{p}}{C_{v}} = γ$ in terms of degrees of freedom (n) is given by

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$(1 + \frac{2}{n})$

$(1 + \frac{n}{2})$

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Detailed Solution

$For n degrees of freedom, C_{v} = \frac{n}{2} R$

$Also, C_{p} - C_{v} = R$

$C_{p} = C_{v} + R = \frac{n}{2} R + R$

$C_{p} = (\frac{n}{2} + 1) R$

$γ = \frac{C_{p}}{C_{v}} = \frac{(\frac{n}{2} + 1) R}{(n / 2) R} = \frac{n + 2}{n} ∴ γ = 1 + \frac{2}{n}$

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The ratio of the specific heats $\frac{C_{p}}{C_{v}} = γ$ in terms of degrees of freedom (n) is given by