Obtain the formula for the coefficient of performance of carnot engine.

Explanation

Efficiency in cyclic process `eta=1-Q_2/Q_1`
and efficiency of carnot engine `eta=1-T_2/T_1`
`therefore Q_2/Q_1=T_2/T_1 rArr Q_1/Q_2 =T_1/T_2`
Expanding this `therefore (Q_1-Q_2)/Q_2=(T_1-T_2)/T_2`
Reversing ` therefore Q_2/(Q_1-Q_2)=T_2/(T_1-T_2)`
But `Q_2/(Q_1-Q_2)` is called coefficient of performance `alpha`.
`therefore alpha=T_2/(T_1-T_2)`