A diatomic gas (γ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

Solution

Physics sir · 4 steps

At constant pressure, work is nRΔ T and heat is nCₚΔ T, so their ratio is fixed by γ.

1. Work at constant pressure. For an isobaric process W = PΔ V = nRΔ T. So nRΔ T = 400 J.
2. Heat at constant pressure. Heat given is Q = nCₚΔ T, with Cₚ = (γ R)/(γ - 1). Dividing Q by W cancels n, R and Δ T.

   Q/W = Cₚ/R = γ/(γ - 1) = 1.4/0.4 = 3.5

3. Check with first law. Δ U = nCᵥΔ T = W/(γ - 1) = 400/0.4 = 1000 J. Then Q = Δ U + W = 1000 + 400 = 1400 J, the same result.
4. So. Q = 3.5 × 400 = 1400 J.

The common slip: 1000. Using Cᵥ instead of Cₚ gives only the change in internal energy, 1000 J. The gas also does 400 J of work, so add it to get the heat.

The idea to keep. In an isobaric process Q : Δ U : W = Cₚ : Cᵥ : R. For a diatomic gas that is 7 : 5 : 2, so any one of them gives the other two.

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