Expansion during heating:

The top of a lake gets frozen at a place where the surrounding air is at a temperature of $-20\,^oC$. Then

The amount of heat needed to heat $200 \ g$ of ice at $-10^{\circ}C$ to convert it into water at $30^{\circ}C$ is:
Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$
Specific heat capacity of water $= 4186 \ J \ kg^{-1} \ K^{-1}$
Latent heat of fusion of ice $= 3.35 \times 10^5 \ J \ kg^{-1}$ (in $J$)

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1 \, g/s$. It melts completely in $100 \, s$. The rate of rise of temperature thereafter will be ........ $^\circ C/s$ (Assume no loss of heat.)

The pressure applied from all directions on a cube is $P$. How much should its temperature be raised to maintain the original volume? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$.

The heat required to convert $8 \ g$ of ice at a temperature of $-20^{\circ}C$ to steam at $100^{\circ}C$ is (Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$,specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$,latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$ and latent heat of steam $= 2.268 \times 10^6 \ J \ kg^{-1}$) (in $kJ$)