A diatomic gas, having Cₚ = 7/2R and Cᵥ = 5/2R, is heated at constant pressure. The ratio dU : dQ : dW :

Solution

Physics sir · 4 steps

At constant pressure, dQ goes with Cₚ and dU with Cᵥ, and the work is whatever is left over.

1. Heat supplied. At constant pressure, for n moles warmed by dT, the heat taken in is dQ = nCₚ dT = 7/2nR dT.
2. Internal energy. For an ideal gas, U depends only on temperature, so in any process dU = nCᵥ dT = 5/2nR dT.
3. Work done. The first law gives dW = dQ - dU = 7/2nR dT - 5/2nR dT = nR dT. This matches P dV = nR dT at constant pressure.

   dU : dQ : dW = 5/2 : 7/2 : 1 = 5 : 7 : 2

4. So. Multiplying through by 2 gives the ratio 5 : 7 : 2, which is option (c).

The idea to keep. In an isobaric process, dQ : dU : dW = Cₚ : Cᵥ : R. For any ideal gas, the work is just Cₚ - Cᵥ = R per mole per kelvin.

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