10 min readConcept sheetSection A objective (2 marks, true or false on refrigerators); Section B very short answer (2 marks) or short answer (3 marks): statements of the second law and the parts of a heat engine

Second law of thermodynamics, heat engines and refrigerators

No engine turns all its heat into work, and heat never flows from cold to hot on its own. That is the second law, in Kelvin-Planck and Clausius forms.

Kelvin-Planck statementNo system can take heat from a source at one temperature and convert all of it into work

Clausius statementHeat cannot pass from a colder body to a hotter body by itself, without external work

Heat engineSource (hot, T₁) → working substance → sink (cold, T₂); work W = H₁ − H₂

Efficiencyη = W/H₁ = 1 − H₂/H₁; always less than 1

Why we need a second law

The first law only balances energy. It would allow heat to flow from a cold body to a hot one, but this never happens by itself. It would also allow the heat in a target to throw a bullet back out, which never happens either. The second law of thermodynamics gives the direction of natural processes and the limit on turning heat into work. It comes from long experience with engines and refrigerators.

How a heat engine works

The engine does work W = H₁ − H₂. Its **efficiency** is η = W/H₁ = 1 − H₂/H₁. Steam engines, petrol and diesel engines and gas turbines all follow this plan.

Two statements of the second law

Kelvin-Planck statementIt is impossible for any system to take heat from a source at one fixed temperature and convert all of it into work. Every engine must reject some heat to a sink, so no engine can be 100% efficient. It is based on heat engines.

Clausius statementIt is impossible for any process to have, as its only result, the transfer of heat from a colder body to a hotter body. External work is always needed, so a refrigerator cannot run without power. It is based on refrigerators.

A refrigerator: a heat engine run backwards

A refrigerator moves heat from a cold place to a warm place by using work. Inside, a liquid called the refrigerant evaporates in coils around the freezer and takes heat H₂ from the food. An electric compressor does work W on the refrigerant vapour, which makes it hot. In the coils at the back, it gives out heat H₁ = H₂ + W to the room and turns back to liquid. So heat is taken from the inner chamber and given to the room. With the door left open in a closed room, the fridge takes H₂ from the room but gives back H₂ + W. So the room slowly gets warmer.

How to draw a heat engine and a refrigerator

1
Heat engine: draw a box at the top labelled Source, T₁ and a box at the bottom labelled Sink, T₂.
2
Draw a circle between them labelled Engine (working substance).
3
Draw an arrow H₁ from the source down into the engine, and an arrow H₂ from the engine down to the sink.
4
Draw an arrow W out of the side of the engine, and write W = H₁ − H₂.
5
Refrigerator: draw the same layout, with Room (hot), T₁ at the top and Inside of the fridge (cold), T₂ at the bottom.
6
Draw the arrows the other way: H₂ up from the cold box into the device, and W in from the side (electric supply). Then draw H₁ = H₂ + W up into the room.

Worked example: efficiency of an engine

Problem

In each cycle an engine takes 1000 J of heat from its source and rejects 700 J to its sink. Find (a) the work done per cycle, (b) the efficiency.

Working

(a) W = H₁ − H₂ = 1000 J − 700 J = 300 J.
(b) η = W/H₁ = 300 J ÷ 1000 J = 0.30.

Answer

(a) 300 J per cycle; (b) 0.30, that is 30%. The other 70% of the heat goes to the sink, as the Kelvin-Planck statement says it must

In real life

A refrigerator needs electric power to pump heat from the food out through its warm back coils, as the Clausius statement says. Every car, bus and tractor engine wastes part of its fuel's heat through the exhaust and radiator, as Kelvin-Planck predicts.

Exam angle

2 marks: “State the Kelvin-Planck and Clausius statements of the second law of thermodynamics.” Kelvin-Planck: no system can take heat from one source and convert all of it into work. Clausius: heat cannot pass from a colder to a hotter body as the only result, without external work.

2 marks: “Name the three essential parts of a heat engine and define its efficiency.” Source (hot body), working substance and sink (cold body). Efficiency η = work done ÷ heat taken from the source = 1 − H₂/H₁.

2 marks: “A working refrigerator is left with its door open in a closed room. Will the room cool down? Explain.” No, it slowly warms. The fridge takes heat H₂ from the room but gives back H₂ + W at its coils, so the work W is added to the room.

Remember it

An engine needs three S's: Source, Substance, Sink. Kelvin-Planck: no perfect engine. Clausius: no fridge without power.