A diatomic gas follows the equation PV^m = co | vedclass

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(D) For a process $PV^m = 	ext{constant}$,the molar heat capacity $C$ is given by the formula: $C = C_V + \frac{R}{1-m}$.For a diatomic gas,the molar

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$5/3$

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(D) For a process $PV^m = 	ext{constant}$,the molar heat capacity $C$ is given by the formula: $C = C_V + \frac{R}{1-m}$.For a diatomic gas,the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.Given that the molar heat capacity $C = R$,we substitute the values into the formula:$R = \frac{5}{2}R + \frac{R}{1-m}$.Subtracting $\frac{5}{2}R$ from both sides:$R - \frac{5}{2}R = \frac{R}{1-m}$.$-\frac{3}{2}R = \frac{R}{1-m}$.Dividing by $R$ (assuming $R 
eq 0$):$-\frac{3}{2} = \frac{1}{1-m}$.Taking the reciprocal of both sides:$-\frac{2}{3} = 1 - m$.Rearranging for $m$:$m = 1 + \frac{2}{3} = \frac{5}{3}$.Therefore,the value of $m$ is $5/3$.

$A$ diatomic gas follows the equation $PV^m =$ constant during a process. What should be the value of $m$ such that its molar heat capacity during the process is equal to $R$?

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