(a) A bootstrap cooling system of 9 TR capacity is employed in an aeroplane . The ambient air temperature and pressure is $20^{\circ} \mathrm{C}$ and 0.86 bar respectively. The pressure of air increases from 0.86 bar to I bar due to ramming action of air. The pressure of the air discharged from the main compressor 3.2 bar. The discharge pressure of air from the auxiliary compressor is 4.2 bar. The isentropic efficiency of each compressor is $82 \%$, while that of turbine is $86 \% .45 \%$ of the enthalpy of air discharged from the main compressor is removed in the first heat exchanger and 32 percent of the enthalpy of air discharged from the auxiliary compressor is removed in the second heat exchanger using rammed air. Assuming ramming action to be isentropic the required cabin pressure of 0.92 bar and temperature of the air leaving the cabin not more than $21^{\circ} \mathrm{C}$, find
Explanation
The power required to operate the system is directly proportional to the mass flow rate of air, specific heat capacity of air, and the temperature difference between the air discharged from the main and auxiliary compressors. The COP of the system is a measure of the efficiency of the system and is calculated by dividing the heat absorbed from the cabin by the work done by the system.
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