A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be (Given gas constant R = 8.3 J K$$^{-1}$$ mol$$^{-1}$$)

A cylinder of fixed capacity 44.8 litres contains helium at STP. We need the heat to raise the temperature by 20°C.

First, at STP, 1 mole of an ideal gas occupies 22.4 litres.

$$n = \frac{44.8}{22.4} = 2 \text{ moles}$$

Next, the cylinder has fixed capacity (constant volume), and helium is a monatomic ideal gas:

$$C_V = \frac{3}{2}R = \frac{3}{2} \times 8.3 = 12.45 \text{ J K}^{-1}\text{mol}^{-1}$$

Finally, we calculate the heat required:

$$Q = nC_V\Delta T = 2 \times 12.45 \times 20 = 498 \text{ J}$$

The correct answer is Option C: 498 J.