Heat Engines (DP IB Physics: HL): Revision Note

Heat Engines

• A heat engine is a device that converts thermal energy into mechanical work

• Heat engines operate through a series of thermodynamic processes which form a closed cycle

  • A closed cycle is one in which the system returns to its initial state

• A simple heat engine consists of a gas in a cylinder with a piston

A simple heat engine converts thermal energy into mechanical work

• The steps in the operation of a cyclic heat engine process are:

1. Extract heat from a hot reservoir

   • A hot reservoir (a source of thermal energy) at a high temperature $T_H$ transfers heat $Q_H$ into the engine

2. Use some of the extracted heat to perform work

   • The gas does mechanical work as it expands which pushes the piston out

3. Release excess heat into a cold reservoir

   • The gas is allowed to cool at constant volume, meanwhile, heat $Q_C$ is released to the surroundings

   • Some of the energy transferred into the engine is released into a cold reservoir (a sink for excess heat) at a lower temperature $T_C$

4. Repeat cycle

   • Once the heat has been extracted, the piston is pushed down to compress the gas back to its original state

   • The process can then be repeated as many times as needed, continuously converting heat into mechanical work 

• For a cyclic heat engine process, the p-V diagram will form a closed loop

• The area inside the loop is equal to the net work done during one cycle

• The net work done by the engine is:

$∆W_{out}=Q_H-Q_C$

• Where:

  • $∆W_{out}$ = useful work output of the heat engine (J)

  • $Q_H$ = heat transferred from hot reservoir to engine (J)

  • $Q_C$ = heat transferred from engine to cold reservoir (J)

Efficiency of Heat Engines

• The goal of a heat engine is to transfer thermal energy into useful mechanical work as efficiently as possible

• The thermodynamic efficiency of a heat engine can be calculated using

efficiency = $\frac{usefulworkoutput}{totalenergyinput}$

$\eta =\frac{W_{out}}{Q_H}=\frac{\left(Q_H-Q_C\right)}{Q_H}$

$\eta =1-\frac{Q_C}{Q_H}$

• Where:

  • $\eta$ = efficiency of a heat engine

  • $W_{out}$ = useful work output (J)

  • $Q_H$ = total energy input from the hot reservoir (J)

  • $Q_C$ = energy lost to the cold reservoir (J)