Identify the process

The gas is in a rigid container, so volume is constant.

Hence, $W = \\int P\,dV = 0$ and the heat supplied goes entirely into changing internal energy: $Q = n C_V \Delta T$

Heat capacity of a diatomic gas

For a rigid diatomic ideal gas (ignoring vibrational modes in this temperature range), $C_V = \frac{5}{2}R$

Given data

• Number of moles: $n = 4$
• Temperature rise: $\Delta T = 50^\circ C - 0^\circ C = 50\,K$

Compute heat required

$Q = n C_V \Delta T$ $Q = 4 \times \frac{5}{2}R \times 50$

Simplifying, $Q = 4 \times 125R = 500R$

Match with options

$Q = 500R$

So the correct option is A.