Question

The efficiency of a carnot engine is `(1)/(6)`. If the temperature of the sink is reduced by 62 K, the efficiency becomes `(1)/(3)`. The temperature of the source and the sink in the first case are respectively.
A. 372 K, 290 K
B. 372 K, 310 K
C. 744 K, 310 K
D. 744 K, 290 K

Answer 1

Correct Answer - B
`(1)/(6)=1-(T_2)/(T_1)implies(T_2)/(T_1)=1-(1)/(6)=(5)/(6)` …(i)
`(1)/(3)=1-(T_2-62)/(T_1)implies(T_2-62)/(T_1)=(2)/(3)` .(ii)
`(i)/(ii)`
`(T_2)/(T_2-62)=((5)/(6))/((2)/(3))=(5)/(4)`
`4T_2=5T_2-310`
`T_2=310K`
`(T_2)/(T_1)=(5)/(6)implies(310)/(T_1)=(5)/(6)`
`T_1=(6)/(5)xx310=372K`