$10\,gm$ of ice at $0\,^oC$ is mixed with $'m'\,gm$ of water at $50\,^oC$ . ........ $gm$ is minimum value of $m$ so that ice melts completely. ( $L_f = 80\,cal/gm$ and $S_W = 1\,cal/gm-\,^oC$ )

A water heater of power $2000\,W$ is used to heat water. The specific heat capacity of water is $4200\,J\,kg ^{-1}\, K ^{-1}$. The efficiency of heater is $70 \%$. Time required to heat $2\,kg$ of water from $10^{\circ}\,C$ to $60^{\circ}\,C$ is $..........s$. (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

A vessel contains $110\,\,g$  of water. The heat capacity of the vessel is equal to $10\,\,g$ of water. The initial temperature of water in vessel is $10\,^oC.$  If $220\,\,g$  of hot water at $70\,^oC$  is poured in the vessel, the final temperature neglecting radiation loss, will be nearly equal to ........ $^oC$

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.)

Water is used to cool radiators of engines in car because

An unknown metal of mass $192\, g$ heated to a temperature of $100\,^oC$ was immersed into a brass calorimeter of mass $128\, g$ containing $240\, g$ of water at a temperature of $8.4\,^oC$. Calculate the specific heat of the unknown metal if water temperature stabilizes at $21.5\,^oC$. (Specific heat of brass is $394\, J\, kg^{-1}\, K^{-1}$) ......... $J\, kg^{-1}\, K^{-1}$