Fig shows a schematic diagram of Bell-Coleman refrigerator (reverse Brayton or joule cycle). This refrigeration system components consists of a compressor, cooler, Expander, and refrigerator. In this process, heat absorption and rejection follows at the constant pressure; the compression and expansion of process are isentropic.

Read: Advantages and Disadvantages of Air/ Bell Coleman Refrigeration System

### Different process in Bell-Coleman refrigeration

Fig show P-V and T-S diagram of bell coleman refrigerator. Here P

_{1}, V

_{1}, T

_{1}, S

_{1}represents the pressure, volume, temperature, entropy of air respectively at point 1. And so on. It represents the corresponding condition of air when it passed through the component.

**1-2: Isentropic Compression**

The Air drawn from refrigerator to air compressor cylinder where it compressed isentropically (constant entropy). No heat transfer by the air. During compression, the volume decreases while the pressure and temperature of air increases.

**2-3: Constant pressure cooling process.**

The warm compressed air is then passed through cooler, where it cooled down at constant pressure.

The heat rejected per kg of air during this process is equal to

q

_{2-3}= Cp(T

_{2}-T

_{3})

**3-4: isentropic expansion**

No heat transfer takesplcae. The air expands isentropically in expander cylinder. During expansion, the volume increases, Pressure P3 reduces to P

_{4}. (P

_{4}= atmospheric pressure). Temperature also falls during expansion from T

_{3}-T

_{4}.

**4-1: Constant pressure expansion**

Heat transfer from the refrigerator to air. The temperature increases from T

_{4}to T

_{1}. Volume increases to V

_{4}due to heat transfer. Heat absorbed by air per kg during this process is equal to

q

_{4-1}= Cp(T

_{1}-T

_{4})

**-**COP of Air Refrigerator working on reversed Carnot cycle with PV and Ts diagram

**-**Mechanism and working of vapour compression refrigeration system - with PV and TS diagram

### Equation of Coefficient of performance (COP) of Bell Coleman cycle

Heat absorbed during cycle per kg of air q_{4-1}= Cp(T

_{1}-T

_{4})

Heat rejected during cycle per kg of air q

_{2-3}= Cp(T

_{2}-T

_{3})

Then the work done per kg of air during the cycle is = Heat rejected – Heat absorbed

= Cp(T

_{2}-T

_{3}) - Cp(T

_{1}-T

_{4})

Coefficient of performance;

For isentropic expansion process 3-4

Since, P2 = P3 and P1 = P4, therefore from equation (ii) and (iii)

Substitute equation (iv) in (i)

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