# Bell Coleman Cycle with PV and TS diagram

The Bell Coleman Cycle is a refrigeration cycle where the working fluid is air which is compressed and expanded but do not change state.

This cycle is the modification of reverse Carnot cycle. Only difference between reverse Carnot cycle and Bell Coleman Cycle is that in Carnot Cycle there are two isothermal processes which are replaced by two isobaric processes in in Bell Coleman Cycle.

The above figure shows the different processes in a Bell Coleman Cycle.Bell Coleman Cycle consists of a compressor, cooler, expander and refrigerator. In this cycle, the process of compression and expansion of gas is isentropic and heat absorption and rejection of heat takes place at constant pressure i.e isobaric process.

### PV and TS diagram of Bell Coleman Cycle

Above figure shows PV and TS diagram of Bell Coleman Cycle .Here P1 , V1 , T1, S1 represents volume, pressure ,temperature and entropy respectively at point 1 and so on.

Below is the elaboration of four steps of Bell Coleman Cycle :-

i) 1-2 : Isentropic Compression :-
This is the first step of Bell Coleman Cycle. In this step, air is drawn from refrigerator to compressor cylinder where it is compressed isentropically. No heat is transferred during this process. As the air is compressed, the volume decreases from V1 to V2 ,pressure increases from P1 to P2 and temperature increases T1 to T2 but entropy remains constant as no heat is transferred.

ii) 2-3 : Adiabatic Cooling process :-
After Isentropic compression, the warm air is passed through cooler where it is cooled adiabatically i.e at constant pressure. This cooler can be an air cooled or water cooled cooler. In most of the cases water cooled cooler is used. In this cooling process, pressure will remain contsant but temperature will decrease,volume will decrease and entropy will also decrease.

iii) 3-4 : Isentropic Expansion :-
In this step , the cooled air is expanded isentropically. Since air is expanded , therefore volume will increase and pressure will decrease.
As this process is isentropic entropy will remain constant and temperature will decrease.

iv) 4-1 : Adiabatic Refrigeration :-
It is the last step of Bell Coleman Cycle. In this step the cooled and expanded air absorbs heat from the refrigerator. Heat is transferred from refrigerator to air. In this process, the air expands due to heat from volume V4 to V1 , temperature increases from T4 to T1 and entropy will also increase fromt S4 to S1.