A-level Chemistry/AQA/Module 5/Thermodynamics/Heat Engines

The Carnot Cycle

The Carnot Cycle is named after its discoverer,Sadi Carnot The Carnot Cycle is the most efficient heat engine that could be built. It converts heat energy from a heat source into work. Or if run in reverse, converts work into the movement of heat, i.e. a refrigerator. In a Carnot Cycle all Processes are reversible.

Steps in a Carnot Cycle

1. Isothermal Expansion at T₁ (The higher temperature). During this step work is done by heat being absorbed from a heat source.
2. Adiabatic Expansion from T₁ to T₂. No heat enters or leaves the system during this step. Work is done on the surroundings in this step.
3. Isothermal Compression at T₂. Heat flows into a heat sink during this step as the surroundings do work on the gas.
4. Adiabatic Compression from T₂ to T₁. Here the surroundings again do work on the system, compressing the gas and raising its temperature.

Efficiency of a Carnot Cycle

The Efficiency η is defined for heat engines as the amount of work done by the process divided by the Heat Input.

As energy must be conserved, the Work is equal to the heat in minus the heat out.

$W=q_{1}-q_{2}$

So the efficiency is equal to

$\eta ={\frac {q_{1}-q_{2}}{q_{1}}}$

This means that the efficiency of a Heat Engine Increases with higher heat source and with a cooler Heat Sink.

$\eta =1-{\frac {q_{2}}{q_{1}}}$ ${\frac {q_{2}}{q_{1}}}={\frac {T_{2}}{T_{1}}}$

so finally

$\eta =1-{\frac {T_{2}}{T_{1}}}$

And as the heat in and out is proportional to the Temperature of the Source and Sink.

Refrigeration and Coefficient of Performance

When a Carnot Cycle is run in reverse, it becomes a fridge, taking heat from the 'sink', and giving it to the 'source'. The coefficient of Performance is defined as

$C={\frac {q_{1}}{W}}$ $C={\frac {q_{1}}{q_{1}-q_{2}}}$

Reversible Process'

A reversible process is one where the entropy of the system and surroundings doesn't increase.