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

Heat engine operates at initial temperature `=100^(@)C+273=373K`
Final temperature `=300^(@)C+273=573 K`
At melting point `=273K`
`"Efficiency "eta=1-(T_(2))/(T_(1))=1-(272)/(573)=0.3491 , eta=34.9%`
(a) By decreasing the cold reservoir, efficiency
`T_(1)=350^(@)C+273=623K, T_(2)=100^(@)C+273=373K`
`eta=1-(T_(2))/(T_(1))=1-(323)/(573)=0.436`
`eta=43.6%`
(b) By increasing the temperature of hot reservoir, efficiency,
`T_(1)=350^(@)C+273=623K, T_(2)=100^(@)C+273=373K`
`eta=1-(T_(2))/(T_(1))=1-(373)/(623)=0.401`
`eta=40.12%`
Method (a) More efficiency than method (b).