A Carnot engine has efficiency 1 5 . Efficiency becomes 1 3 when the temperature of sink is decreased by 50 K . Temperature of the sink ( in K ) is

Step-by-step solution

The efficiency of the Carnot engine η = Work   output Heat   input = W Q H or η = Q H - Q L Q H = 1 - Q L Q H Also we can show that Q L Q H = T L T H ∴   η = 1 - T L T H   where T L is temperature of sink and T H is the temperature of hot reservoir. According to question   1 5 = 1 - T L T H ...( i ) 1 3 = 1 - T L - 50 T H ...( ii ) From Eq. ( i ) T L T H = 4 5 ⇒ T H = 5 4 T L Substituting value of T H in Eq. ( ii ), we get 1 3 = 1 - T L - 50 5 4 T L or  &#160