Efficiency of a heat engine whose sink is at temperature of 300 K is 40% . To increase the efficiency to 60 % keeping the sink temperature same, the source temperature must be increased by

Options

A. 750 K
B. 500 K
C. 250 K
D. 1000 K

Answer

C

Explanation

Efficiency of heat engine ,
`eta = 1 - T_(2)/T_(1)`
`implies T_(2)/T_(1) = 1-eta`
`300/T_(1) = 1-0.4` `( because T_(2) = 300 K)`
` T_(1) = 500 K`
`eta^(ast) = 1-T_(2)/T_(1)^(ast)` `(because T_(2) =const)`
`T_(2)/T_(1)^(ast) = 1 - eta^(ast) = 1- 0.6`
`implies T_(1)^(*) = (300)/(1- 0.6) =750 K`