Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Thermodynamics · Topic: Thermodynamics – General · Marks: 2 · Difficulty: Medium
The figure below describes how a Carnot engine works. It starts from the adiabatic compression step denoted by
(a)AB
(b)BC
(c)DC
(d)AD
Answer
Answer: B ✓ checked by 4AB · confidence medium
The source book printed no answer; this one was worked out and checked — see the explanation.
Key was missing. In the V-vs-P figure the flat curves AD and BC are adiabats and the steep sides AB and DC are isotherms; DC (higher P) is the hot isotherm. Engine cycle: C→D hot isothermal expansion, D→A adiabatic expansion, A→B cold isothermal compression, B→C adiabatic compression. So the adiabatic compression step is BC.
Explanation
Here V is plotted against P. An isotherm (V = nRT/P) has slope −V/P, while an adiabat (V ∝ P^{−1/γ}) has the flatter slope −V/(γP). So the flat curves AD and BC are adiabats and the steep sides AB and DC are isotherms. DC lies at higher P for the same V, so it is the hot isotherm and AB is the cold one.
Engine cycle: C→D isothermal expansion at T_hot, D→A adiabatic expansion (V rises, gas cools), A→B isothermal compression at T_cold, then B→C adiabatic compression (V falls, P rises, gas heats from T_cold to T_hot). The adiabatic compression step is BC, option (b).