Final answer:
In each of the given two-step paths, the argon gas undergoes different thermodynamic processes. The calculations for Q, W, ΔU, and ΔH are explained for each step and the overall process for each path.
Step-by-step explanation:
In each of the given two-step paths, the argon gas undergoes different thermodynamic processes. Let's calculate Q, W, ΔU, and ΔH for each step and the overall process for each path:
(a) Isothermal compression followed by isobaric heating:
- Step 1: Isothermal compression (Q = 0, W < 0, ΔU < 0, ΔH < 0)
- Step 2: Isobaric heating (Q > 0, W > 0, ΔU > 0, ΔH > 0)
- Overall process: Q = Q1 + Q2, W = W1 + W2, ΔU = ΔU1 + ΔU2, ΔH = ΔH1 + ΔH2
(b) Adiabatic compression followed by isobaric heating or cooling:
- Step 1: Adiabatic compression (Q = 0, W < 0, ΔU < 0, ΔH < 0)
- Step 2: Isobaric heating or cooling (Q ≠ 0, W ≠ 0, ΔU ≠ 0, ΔH ≠ 0)
- Overall process: Q = Q1 + Q2, W = W1 + W2, ΔU = ΔU1 + ΔU2, ΔH = ΔH1 + ΔH2
(c) Adiabatic compression followed by isochoric heating or cooling:
- Step 1: Adiabatic compression (Q = 0, W < 0, ΔU < 0, ΔH < 0)
- Step 2: Isochoric heating or cooling (Q ≠ 0, W ≠ 0, ΔU ≠ 0, ΔH ≠ 0)
- Overall process: Q = Q1 + Q2, W = W1 + W2, ΔU = ΔU1 + ΔU2, ΔH = ΔH1 + ΔH2
(d) Adiabatic compression followed by isothermal compression or expansion:
- Step 1: Adiabatic compression (Q = 0, W < 0, ΔU < 0, ΔH < 0)
- Step 2: Isothermal compression or expansion (Q = 0, W ≠ 0, ΔU ≠ 0, ΔH ≠ 0)
- Overall process: Q = Q1 + Q2, W = W1 + W2, ΔU = ΔU1 + ΔU2, ΔH = ΔH1 + ΔH2