The Bell-Coleman cycle is an example of _________.

Explanation:

A Bell-Coleman air refrigeration cycle works on the reverse Brayton cycle.

The relationship between the various temperature of the cycle is given by the isentropic relationship applied to both compression and expansion processes:

\({r_p} = \frac{{{P_2}}}{{{P_1}}} = {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^{\frac{\gamma }{{\gamma - 1}}}} = {\left( {\frac{{{T_3}}}{{{T_4}}}} \right)^{\frac{\gamma }{{\gamma - 1}}}}\)

\(\frac{{{T_2}}}{{{T_1}}} = \frac{{{T_3}}}{{{T_4}}}\;or\;\frac{{{T_2}}}{{{T_3}}} = \frac{{{T_1}}}{{{T_4}}}\)

\({\rm{COP}} = \frac{{{\rm{Refrigeration\;effect}}}}{{{\rm{Net\;work\;input}}}} = \frac{{{\rm{Heat\;added}}}}{{{\rm{Net\;work\;input}}}}\)

Refrigeration effect: Q1 = Cp(T1 – T4)

Compressor work, W1 = Cp(T2 – T1)

Turbine work, W2 = Cp(T3 – T4)

\(COP = \frac{{{Q_1}}}{{{W_1} - {W_2}}} = \frac{{\left( {{T_1} - {T_4}} \right)}}{{\left( {{T_2} - {T_1}} \right) - \left( {{T_3} - {T_4}} \right)}} = \frac{{\left( {{T_1} - {T_4}} \right)}}{{\left( {{T_2} - {T_3}} \right) - \left( {{T_1} - {T_4}} \right)}} = \frac{1}{{\frac{{{T_2} - {T_3}}}{{{T_1} - {T_4}}} - 1}}\)

\(COP = \frac{1}{{\frac{{{T_2} - {T_3}}}{{{T_1} - {T_4}}} - 1}} = \frac{1}{{\frac{{{T_3}}}{{{T_4}}}\left( {\frac{{\frac{{{T_2}}}{{{T_3}}} - 1}}{{\frac{{{T_1}}}{{{T_4}}} - 1}}} \right) - 1}} = \frac{1}{{\frac{{{T_3}}}{{{T_4}}} - 1}} = \frac{1}{{{{\left( {{r_p}} \right)}^{\frac{{\gamma - 1}}{\gamma }}} - 1}}\)

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