A rigid container holds 5 g of a gas, which is heated from 15^ ^ ^...

For a rigid container, the volume remains constant, so the work done by the gas is zero.

From the first law of thermodynamics, the change in internal energy is equal to the heat supplied at constant volume:

$\Delta U = \Delta Q = m c_v \Delta T$

Substituting the given values:

$\Delta U = 5 \times 0.172 \times (25 - 15)$

$\Delta U = 5 \times 0.172 \times 10 = 8.6 \text{ cal}$

Converting the energy to Joules using the mechanical equivalent of heat $J = 4.2 \text{ J cal}^{-1}$:

$\Delta U = 8.6 \times 4.2 = 36.12 \text{ J}$