The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0° C to 50° C when no work is done is ___________. (R is the universal gas constant).

Solution

Physics sir · 3 steps

No work done means the volume is fixed, so all the heat goes into internal energy: use Cᵥ, not Cₚ.

1. No work. With W = 0, the first law Q = Δ U + W becomes Q = Δ U. Every bit of heat raises the internal energy, which is a constant-volume process.
2. Rigid diatomic. A rigid diatomic molecule has 5 degrees of freedom: 3 translational and 2 rotational, with no vibration. So Cᵥ = 5/2R per mole.

   Q = nCᵥ Δ T = 4 × 5/2R × 50

3. So. A rise from 0°C to 50°C is Δ T = 50 K, so Q = 10R × 50 = 500R. The answer is (a).

The idea to keep. Whenever no work is done, heat equals the change in internal energy, so use nCᵥΔ T. For a rigid diatomic gas Cᵥ = 5/2R.

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