At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

Solution

Physics sir · 4 steps

At constant pressure, compare heat with work: Q/W = Cₚ/R, and Cₚ comes straight from f.

1. Work at constant pressure. For an ideal gas at constant pressure, W = PΔ V = nRΔ T. So nRΔ T = 150 J.
2. Heat capacity from f. With f degrees of freedom, Cᵥ = f/2R and Cₚ = (f/2+1)R. For f = 8, Cₚ = 5R.

   Q/W = (nCₚΔ T)/(nRΔ T) = Cₚ/R = (f+2)/2 = 5

3. Check with first law. Δ U = nCᵥΔ T = 4 × 150 = 600 J, so Q = Δ U + W = 600 + 150 = 750 J.
4. So. The heat absorbed is Q = 5 × 150 = 750 J.

The common slip: 600. Using Cᵥ instead of Cₚ gives only the change in internal energy, 600 J. The gas also does 150 J of work, so add that back.

The idea to keep. In an isobaric process the ratio of heat to work is (f+2)/2, and the ratio of internal energy change to work is f/2. Remember these and such questions take one line.

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