COP Of Air Refrigerator Working On Reversed Carnot Cycle with PV and Ts Diagram

Introduction to the Air Refrigerator working on reversed Carnot cycle

In these type of refrigerator, a reversed Carnot cycle is considered. For a heat engine, the highest possible efficiency is achieved by the Carnot cycle. Similarly in refrigeration cycle highest possible coefficient of performance is obtained when the system is working on reversed Carnot cycle. However, it is not possible to make an engine operating on the Carnot cycle, or it is not possible to make a refrigerating system working on reversed Carnot cycle. This hypothetical heat cycle is used as a standard of comparison.

- Air Refrigerator working on Bell-Coleman cycle with PV and TS diagram (reversed Brayton or Joule Cycle)
- Mechanism and working of a vapour compression refrigeration system - with PV And TS diagram

P-V and T-S Diagrams of reversed Carnot cycle - Process involved

Fig (1) and fig(2) shows the p-v and T-s diagram of a refrigeration system working on reversed Carnot cycle. The process involved in reversed Carnot cycles are as follows

1-2. isentropic compression process
During this stage, air is compressed isentropically. Pressure and temperature increases, the specific volume of decreases. During isentropic compression, there is no heat exchanging (absorb and rejection) takes place by air.

2-3 Isothermal compression
After isentropic compression air again compress isothermally (constant temperature). The pressure increases while specific volume decreases. The heat rejected during isothermal compression per kg of air
q_2-3 =T₃(S₂-S₃) = T₂(S₂-S₃)

3-4. Isentropic expansion process
The air expands isentropically as shown in above figure. Pressure decreases from P₃ to P₄, specific volume increases from v₃ to v₄. The temperature also decreases. There is no heat transfer by air during this process.

4-1. Isothermal expansion process
The air expands at a constant temperature. The pressure of air decreases while the specific volume of air increases. During this process, the heat absorbed by air per kg of air
Q_4-1 = T₄(S₁-S₄) = T₄(S₂-S₃) = T₁(S₂-S₃)

Coefficient of performance of Refrigerator working on reversed Carnot cycle

Read: Coefficient of performance and relative coefficient of performance of refrigeration cycle

Net work done during reversed Carnot cycle per kg of air is = Heat rejected - heat absorbed.
= q_2-3 - q_4-1
T₂(S₂-S₃) - T₁(S₂-S₃)
=(T₂-T₁)(S₂-S₃)
Coefficient of performance (COP)_R = Heat absorbed / Work done = q_4-1/(q_2-3 - q_4-1)