The ratio of specific heats at constant press | vedclass

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Question

(A) We know that the ratio of specific heats is defined as $\gamma = \frac{C_p}{C_V}$.For an ideal gas,the molar heat capacity at constant volume is $

Vedclass · Accepted Answer

$f=\frac{2}{\gamma-1}$

Vedclass · Answer

(A) We know that the ratio of specific heats is defined as $\gamma = \frac{C_p}{C_V}$.For an ideal gas,the molar heat capacity at constant volume is $C_V = \frac{f}{2}R$,where $f$ is the degree of freedom.Using Mayer's relation,the molar heat capacity at constant pressure is $C_p = C_V + R = \frac{f}{2}R + R = \frac{f+2}{2}R$.Substituting these into the expression for $\gamma$:$\gamma = \frac{C_p}{C_V} = \frac{\frac{f+2}{2}R}{\frac{f}{2}R} = \frac{f+2}{f}$.Rearranging the equation to solve for $f$:$\gamma f = f + 2$$\gamma f - f = 2$$f(\gamma - 1) = 2$$f = \frac{2}{\gamma - 1}$.

The ratio of specific heats at constant pressure and at constant volume is $\gamma$. To find out the degree of freedom,the expression is

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