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.)

$M$ grams of steam at $100^{\circ} \mathrm{C}$ is mixed with $200\; \mathrm{g}$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ} \mathrm{C}$ [heat of vaporization of water is $540 \;cal/\mathrm{g}$ and heat of fusion of ice is $80 \;\text { cal/g }]$ the value of $\mathrm{M}$ is

A tap supplies water at $10\,^oC$ and another tap at $100\,^oC$. .......... $kg$ hot water must be taken so that we get $20\, kg$ water at $35\,^oC$ ?

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 $394\, J\, kg^{-1}\, K^{-1}$) ......... $J\, kg^{-1}\, K^{-1}$

The temperature of equal masses of three different liquids ${x}, {y}$ and ${z}$ are $10^{\circ} {C}, 20^{\circ} {C}$ and $30^{\circ} {C}$ respectively. The temperature of mixture when ${x}$ is mixed with ${y}$ is $16^{\circ} {C}$ and that when ${y}$ is mixed with $z$ is $26^{\circ} {C}$. The temperature of mixture when $x$ and $z$ are mixed will be ...... $^{\circ} {C}$

$50 \,g$ ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \,g$ water at $30^{\circ} C$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is .......... $g$