Main compressor exit pressure is 3.5 bar, and exit pressure of secondary compressor exit pressure is 4.5 bar. The cabin is required to be maintained at 1 bar and $25^o$C. Isentropic efficiency of each compressor is 85% and that of cooling turbine is 90%. The effectiveness of both heat exchangers is 60%. Find:

i) Mass flow rate of air passing through the cabin

ii) Power required

iii) COP of the system. Assume Cp = 1.01 KJ/KgK.

T1 = 15+273 = 288K

Consider the ramming action: ${T_2/T_1 }$=$(p_2/p_1 )^{(1.4-1)/1.4}$

${T_2/288}=(1.1/0.9)^{(1.4-1)/1.4}$

$T_2=305 K$

Consider the main compressor:

${T_3/T_2} =(p_3/p_2 )^{(γ-1)/γ}$

${T_3/305}=(3.5/1.1)^{(1.4-1)/1.4}$

${T_3=424.5K}$ Fig.1 Process of Air refrigeration.

Efficiency of compressor I: