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(A) The change in internal energy is given by the formula: $\Delta U = n C_v \Delta T$ ... $(i)$Given that $\frac{C_P}{C_v} = \gamma$ and $C_P - C_v =

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

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(A) The change in internal energy is given by the formula: $\Delta U = n C_v \Delta T$ ... $(i)$Given that $\frac{C_P}{C_v} = \gamma$ and $C_P - C_v = R$,we can write $C_v = \frac{R}{\gamma - 1}$.Substituting this into equation $(i)$,we get: $\Delta U = n \left( \frac{R}{\gamma - 1} \right) \Delta T$.Since the pressure $P$ is constant,we use the ideal gas law $PV = nRT$,which implies $P \Delta V = nR \Delta T$.Substituting $P \Delta V$ for $nR \Delta T$ in the expression for $\Delta U$,we get: $\Delta U = \frac{P \Delta V}{\gamma - 1}$.Given that the volume changes from $V$ to $2V$,$\Delta V = 2V - V = V$.Therefore,$\Delta U = \frac{PV}{\gamma - 1}$.

The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is (where $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume):

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