If R = universal gas constant, the amount of heat needed to raise the temperature of 5 mol of an ideal monoatomic gas from 273 K to 373 K when no work is done is :

750 R

The correct answer is Option 1: 750 R

Since the question states that no work is done ($W = 0$), the volume of the gas remains constant (isochoric process). In such a process, the heat supplied ($Q$) is equal to the change in internal energy ($\Delta U$).

For an ideal monoatomic gas at constant volume: $Q = nC_v\Delta T$

Where: $C_v$ (Molar specific heat at constant volume) for a monoatomic gas = $\frac{3}{2}R$

Given Values:

• Number of moles ($n$) = $5\text{ mol}$

• Temperature change ($\Delta T$) = $373\text{ K} - 273\text{ K} = 100\text{ K}$