Suppose a person wants to increase the efficieny of the reversible heat engine that is operating between `100^(@)C` and `300^(@)C`
He had two ways to increase the efficiency .
( a) By decreasing the cold reservoir temperature from `100^(@)C` to `50^(@)C` and keeping the hot reservoir temperature of the hot reservoir from `300^(@)C` to `350^(@)C` by keeping the cold reservoir temperature constnat which is the suitable method ?

Explanation

Temperature of sin `x T_(2) = 100^(@)C + 273 = 373 K`
Temperature of sin `x T_(1) - 300^(@)C + 273 = 573 K`
Efficiency `eta = ?`
`eta = 1 - (T_(1))/(T_(2))`
`eta =1 - (273)/(573)`
`= (573 - 273)/(573) = (300)/(573) = 52 . 3%`
(a ) By decreasing the cold reservoir
`eta = 1- (T_(2))/(T_(1))`
`T_(2) = 50 + 273 = 323 K`
`T_(1) =3 00 + 273 = 573 K`
`eta = 1- (323 )/(573) = (573-323)/( 573)`
`= 0.436 xx 100 = 43 .6%`
( b) By increasing the temperature of hot reservoir
`T_(1) = 350 + 273 = 623 k`
`T_(2) =100 + 273 = 373 k`
`eta = 1 - (T_(2))/(T_(1)) = 1- (373)/(623) = (623 - 373)/( 623)`
`=0.401 xx 100 = 40. 1% `
Method ( a) is more efficient than method ( b)