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(D) At constant pressure, the work done is given by $W = P \Delta V$. For an ideal gas, $PV = nRT$, so $P \Delta V = nR \Delta T$. Thus, $W = nR \Delt

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$\frac{3 \,W}{2}$

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(D) At constant pressure, the work done is given by $W = P \Delta V$. For an ideal gas, $PV = nRT$, so $P \Delta V = nR \Delta T$. Thus, $W = nR \Delta T$. Heat supplied at constant volume is given by $Q = \Delta U = nC_v \Delta T$. For a monoatomic gas, the molar heat capacity at constant volume is $C_v = \frac{3}{2}R$. Substituting this into the heat equation, we get $Q = n \left( \frac{3}{2}R \right) \Delta T = \frac{3}{2} (nR \Delta T)$. Since $W = nR \Delta T$, we substitute $W$ into the equation for $Q$: $Q = \frac{3}{2} W$.

For a monoatomic gas, the work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is

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