Question

The temperatures `T_(1) and T(2)` of two heat reservoirs in an ideal carnot engine are `1500^(@)C and 500^(@)C`. Which of these (a) increasing `T_(1) by 100^(@)C` or (b) decreasing `T_(2) by 100^(@)C` would result in greater improvement of the efficiency of the engine?

Answer 1

Here, `T_(1)= 1500^(@)C= (1500+273)K`
`= 1773K`
`T_(2)= 500^(@)C= 500+273= 773K`
`eta = 1 -(T_(2))/(T_(1))= 1 -(773)/(1773)= (1000)/(1773)`
(a) Increasing `T_(1) by 100^(@)C`
`T_(1)= 1600+273= 1873K, T_(2)=773K`
`eta_(1)= 1 -(T_(2))/(T_(1))= 1 -(773)/(1873)= (1100)/(1873)`
(b) Decreasing `T_(2) by 100^(@)C`
`T_(1)= 1500+273= 1773K`
`T_(2)=(500-100)+273= 673K`
`eta_(2)= 1 -(T_(2))/(T_(1))= 1 -(673)/(1773)= (1100)/(1773)`
Clearly, `eta_(2) gt eta_(1)`. Therefore, (b) is better choice.