Isothermal compression is compression at constant temperature. It is not trivial because liquids are hardly compressible and gases heat up during compression. Gases heat up during relatively fast compression because the pressure work done onto the gas increases its internal energy and therefore its temperature.

Heat Rejection in Carnot Cycle

Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The cycle is named after Nicolas Léonard Sadi Carnot, a French physicist who first proposed it in 1824.

Heat rejection is one of the processes in the Carnot cycle that occurs at a specific stage. Let us discuss this process in detail.

Explanation

The Carnot cycle operates between two heat reservoirs, a hot source and a cold sink, and a working substance, usually a gas or a vapor, undergoes a series of thermodynamic transformations. The cycle is shown in the P-V diagram below:


As the working substance is compressed from state 4 to state 1, it releases heat to the surroundings, which is the heat rejection process. This process occurs during the isothermal compression process, where the temperature of the working substance remains constant, and the pressure decreases.

The heat rejection process can be explained by the following steps:

1. The working substance is initially at state 4, where it has a high temperature and pressure.
2. The substance is compressed isothermally from state 4 to state 3, where heat is rejected to the surroundings.
3. The compressed substance is then allowed to expand adiabatically from state 3 to state 2, where its temperature and pressure decrease.
4. The substance is then expanded isothermally from state 2 to state 1, where heat is absorbed from the surroundings.
5. Finally, the substance is compressed adiabatically from state 1 to state 4, where it returns to its initial state.

Conclusion

In conclusion, the heat rejection process in the Carnot cycle occurs during the isothermal compression process, where the working substance releases heat to the surroundings. This process is essential in converting thermal energy into mechanical energy and is the basis for many practical applications, such as refrigeration and power generation.

During isothermal compression of gas there is no change in internal energy.However work done on the gas is completly dissipated as heat.