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(D) For a polytropic process $PV^n = 	ext{constant}$, the work done $W$ is given by $W = \frac{nR\Delta T}{1-n}$.For a diatomic gas like Hydrogen, th

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$-0.4$

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(D) For a polytropic process $PV^n = 	ext{constant}$, the work done $W$ is given by $W = \frac{nR\Delta T}{1-n}$.For a diatomic gas like Hydrogen, the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.The change in internal energy is $\Delta U = nC_V\Delta T = n(\frac{5}{2}R)\Delta T$.Given the process $PV^2 = 	ext{constant}$, we have $n = 2$.The work done is $W = \frac{nR\Delta T}{1-2} = -nR\Delta T$.The ratio of work done to the change in internal energy is $\frac{W}{\Delta U} = \frac{-nR\Delta T}{n(\frac{5}{2}R)\Delta T} = \frac{-1}{2.5} = -0.4$.

Hydrogen gas is undergoing a process given by $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is

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