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

$5\,\,gm.$  of ice at $0\,^oC$  is dropped in a beaker containing $20\,\,gm.$ of water at $40\,^oC.$ The final temperature will be  ........ $^oC$

Ice at $0^o C$ is added to $200 \,\,g$ of water initially at $70^o C$ in a vacuum flask. When $50\,\, g$ of ice has been added and has all melted the temperature of the flask and contents is $40^o C$. When a further $80\,\,g$ of ice has been added and has all metled, the temperature of the whole is $10^o C$. Calculate the specific latent heat of fusion of ice.[Take $S_w =1\,\, cal /gm ^o C$.]

A mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.

$2\  kg$ ice at $-20^o\ C$ is mixed with $5\  kg$ water at $20^o\ C$. Then final amount of water in the mixture would be ; Given specific heat of ice $= 0.5\ cal/g^o\ C$, specific heat of water $= 1\  cal/g^o\ C$, Latent heat of fusion of ice $= 80\  cal/g$ ........ $kg$

Heat required to convert $5\ kg$ ice at $0\ ^oC$ into water at $100\ ^oC$ is