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

When the temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. The increase in the rms velocity of the gas molecule is

If ambient temperature is 300 K , the rate of cooling at 600 K is $H$. In the same surroundings, the rate of cooling at 900 K is