The P-V diagram of a diatomic gas is a straig | vedclass

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(C) The $P-V$ diagram of the gas is a straight line passing through the origin. Therefore,$P \propto V$,which implies $P = kV$ or $PV^{-1} = 	ext{con

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$3R$

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(C) The $P-V$ diagram of the gas is a straight line passing through the origin. Therefore,$P \propto V$,which implies $P = kV$ or $PV^{-1} = 	ext{constant}$.Comparing this with the polytropic process equation $PV^x = 	ext{constant}$,we get $x = -1$.The molar heat capacity $C$ for a polytropic process is given by the formula $C = \frac{R}{\gamma - 1} + \frac{R}{1 - x}$.For a diatomic gas,the adiabatic index $\gamma = 1.4 = \frac{7}{5}$.Substituting the values: $C = \frac{R}{\frac{7}{5} - 1} + \frac{R}{1 - (-1)}$.$C = \frac{R}{\frac{2}{5}} + \frac{R}{2} = \frac{5R}{2} + \frac{R}{2} = \frac{6R}{2} = 3R$.

The $P-V$ diagram of a diatomic gas is a straight line passing through the origin. The molar heat capacity of the gas in this process will be:

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