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 JK⁻¹-mol⁻¹)

Solution

Physics sir · 3 steps

Fixed capacity means fixed volume, so heat the helium at constant volume and use Cᵥ, not Cₚ.

1. Count the moles. At STP one mole of an ideal gas occupies 22.4 L. So n = 44.8/22.4 = 2 mol.
2. Constant volume. The cylinder cannot expand, so the gas does no work and all the heat goes into internal energy. Helium is monatomic, so Cᵥ = 3/2R.

   Q = nCᵥΔ T = 2 × 3/2 × 8.3 × 20 = 498 J

3. So. A rise of 20 °C is the same as a rise of 20 K, so the heat needed is 498 J, option (c).

The idea to keep. A rigid container means W = 0, so Q = nCᵥΔ T. Get n from the STP volume, and remember Cᵥ = 3/2R for a monatomic gas like He.

Answer from the NTA final answer key. Solution by PrepWiser.