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(D) The change in internal energy $\Delta U$ for an ideal gas is given by the formula $\Delta U = n C_V \Delta T$.From the ideal gas equation,$PV = nR

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$\frac{PV}{\gamma-1}$

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(D) The change in internal energy $\Delta U$ for an ideal gas is given by the formula $\Delta U = n C_V \Delta T$.From the ideal gas equation,$PV = nRT$,so $n R \Delta T = P \Delta V$.Since $C_V = \frac{R}{\gamma-1}$,we can write $\Delta U = n \left( \frac{R}{\gamma-1} \right) \Delta T = \frac{n R \Delta T}{\gamma-1}$.Substituting $n R \Delta T = P \Delta V$,we get $\Delta U = \frac{P \Delta V}{\gamma-1}$.Given that the volume changes from $V$ to $2V$,the change in volume is $\Delta V = 2V - V = V$.Therefore,$\Delta U = \frac{P(V)}{\gamma-1} = \frac{PV}{\gamma-1}$.

The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is given by (where $\gamma = C_P / C_V$):

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