A carnot engine has efficiency `1//5` . Efficiency becomes `1//3` when temperature of sink is decreased by 50 K What is the temperature of sink ?

Options

A. 325 K
B. 375 K
C. 300 K
D. 350 K

Answer

C

Explanation

`eta=1-(T_2)/(T_1) implies 1/5=1-(T_2)/(T_1)" "`…(i)
Now, `1/3=1-((T_2-50))/(T_1)" "`…(ii)
(i) `implies 1/5=1-(T_2)/(T_1) implies (T_2)/(T_1)=1-1/5=4/5`
`implies T_(1)=5/4 T_2`
(ii) `implies 1/3=1-((T_2-50))/(5/4 T_2) implies T_2=300K`.