The temperature difference across two cylindrical rods $A$ and $B$ of same material and same mass are $40^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$ respectively. In steady state, if the rates of flow of heat through the rods $A$ and $B$ are in the ratio 3:8, the ratio of the length of the rods $A$ and $B$ is

The efficiency of Carnot cycle is $\frac{1}{6}$. By lowering the temperature of sink by 65 K , it increases to $\frac{1}{3}$. The initial and final temperature of the sink are

In a cold storage ice melts at the rate of 2 kg per hour when the external temperature is $20^{\circ} \mathrm{C}$. The minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting is (latent heat of fusion of ice $=80 \mathrm{calg}^{-1}$ )

A Carnot engine has the same efficiency between 800 K and 500 K and $x>600 \mathrm{~K}$ and 600 K . The value of $x$ is