Obtain the relation between coefficient of performance and efficiency .

Explanation

Coefficient of performance
`alpha=Q_2/W=Q_2/(Q_1-Q_2) [ because W=Q_1-Q_2]`
`therefore alpha = (Q_2/Q_1)/(1-Q_2/Q_1)`
`therefore alpha=(Q_2/Q_1)/eta`…(1)
Now efficiency of carnot engine based on cyclic process `eta=1-Q_2/Q_1`
`therefore Q_2/Q_1=1-eta`..(2)
`therefore` From equation (1) and (2)
`alpha=(1-eta)/eta`