Describe the Carnot cycle with the help of an indicator diagram. Derive the expression for its efficiency. Why can a Carnot engine not be made in practice?
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Describe the engine. An ideal reversible engine: an ideal gas in a cylinder with insulating walls, a conducting base and a frictionless piston; a source at T₁, a sink at T₂ and an insulating stand.
2 · Draw the P-V diagram. Loop ABCD: isotherm AB at T₁, adiabatic BC, isotherm CD at T₂, adiabatic DA; arrows clockwise; area shaded.
3 · Explain the four steps.
AB: isothermal expansion on the source; heat H₁ taken in.
BC: adiabatic expansion on the stand; the gas cools to T₂.
CD: isothermal compression on the sink; heat H₂ given out.
DA: adiabatic compression on the stand; the gas warms to T₁.
4 · Net work. ΔU = 0 for the cycle, so W = H₁ − H₂ = area ABCD.
5 · Efficiency. η = W/H₁ = 1 − H₂/H₁. For a Carnot engine H₂/H₁ = T₂/T₁, so η = 1 − T₂/T₁.
6 · Why it cannot be built. The isothermal steps need an extremely slow piston and the adiabatic steps an extremely fast one; zero friction and zero heat leak are impossible.
7 · Real life. Power stations use the hottest safe steam and a cold river or cooling tower to raise their efficiency, as η = 1 − T₂/T₁ suggests.
8 · Close in one line. The Carnot engine sets the upper limit on the efficiency of every real engine.
Scoring tip: Label each of the four curves with its process and mark where H₁ enters and H₂ leaves. These labels carry marks in a 5-mark answer.
