Draw the reversed carnot cycle on P-V and T-S diagrams and find out the expression for COP of the cycle. Discuss the factors which affect the COP of the cycle.

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teamques10 ★ 69k

The Carnot refrigerator works on the reversed Carnot cycle. A reversed Carnot cycle using air as working medium is shown on p-v and t-s diagrams. The processes involved during the cycle are:

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Fig. Reversed Carnot Cycle

1. Isentropic compression process- Air is compressed is entropically as shown by curve 1-2 on diagrams. No heat is absorbed or rejected by the air.

2. Isothermal compression process- Air is now compressed isothermally (T2=T3) and the heat rejected per kg of air during the process is given by

$q_{2-3}= \ \ \ area \ \ \ 2-3-3'-2' =T_3 (s_2-s_3 )=T_2 (s_2-s_3 )$

3. Isentropic expansion process- Air is now expanded is entropically as shown by curve 3-4.

4. Isothermal expansion process- Air is expanded isothermally and heat absorbed by air (or heat extracted from cold body) during this process per kg of air is given by

$q_{4-1}=area \ \ \ 4-1-2'-3'=T_4 (s_1-s_4 )=T_4 (s_2-s_3 )=T_1 (s_2-s_3 )$

Therefore, work done during cycle per kg of air

$=\text{heat rejected-heat absorbed}=(q_{2-3})-(q_{4-1}) \\ =T_2 (s_2-s_3 )-T_1 (s_2-s_3 )=(T_2-T_1 )(s_2-s_3 )$

C.O.P. of refrigerator working on reversed Carnot cycle,

$C.O.P_R=\frac{(\text{Heat absorbed})}{(\text{Work done})}=\frac{q_{4-1}}{(q_{2-3}-q_{4-1})}=\frac{T_1 (s_2-s_3 )}{(T_2-T_1 )(s_2-s_3 )} =\frac{T_1}{(T_2-T_1 )}$

Factors which affect the COP of the cycle:

C.O.P. of the reversed Carnot cycle may be improved by decreasing higher temperature i.e. temperature of hot body T2
Increasing lower temperature i.e. temperature of cold body T1 also improves C.O.P.
Although this cycle gives maximum C.O.P. yet it is impossible to achieve this because the isentropic processes of the cycle require high speed while the isothermal processes require an extremely low speed which is impracticable for air or gas.

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