Question

Bell-coleman cycle is used to cool the space. Air is taken into the compressor at 1 bar and ${10}^{\circ }C$. It is compressed with pressure ratio equal to 10. The air is then cooled by ${200}^{\circ }C$. Expansion and compression follow $P{V}^{\frac{1}{4}}=C$. The COP is if R = 0.287 kJ/kg K, $C_p=1.005\text{kJ/kg K}$

• A. 1.975
• B. 1.675
• C. 1.075
• D. 2.075

Answer 1

The correct option is C 1.075

$r_p=10=\frac{P_2}{P_1},T_1=283\text{K}$



$\Rightarrow \frac{T_2}{T_1}={\left(\frac{P_2}{P_1}\right)}^{\frac{1.4-1}{1.4}}$

COP $=\frac{1}{r_p^{}\left(\frac{\gamma -1}{\gamma }\right)-1}$

COP $=\frac{1}{{10}^{\frac{1.4-1}{1.4}}}$

COP $=1.0745$