In the definition of 'calorie' one calorie is the heat required to raise the temperature of $1\  gram$ of water through $1\  ^oC$ in a certain interval of temperature. The temperature interval is

$100 \,gm$ of ice at $0°C$ is mixed with $100\, g$ of water at $100°C.$ What will be the final temperature of the mixture .......... $^oC$

$500\, g$ of water and $100\, g$ of ice at $0\,^oC$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^oC$ is added to it. Then water in the calorimeter is ....... $g$ (Latent heat of ice $\,= 80\, cal/g$, Latent heat of steam $\,= 540\, cal/ g$)

$1\ gm$ of ice at $0^o C$ is mixed with $1gm$ of water at $100^o C$ the resulting temperature will be .......... $^oC$ 

$10\, gm$ of ice at $-20°C$ is dropped into a calorimeter containing $10\, gm$ of water at $10°C;$ the specific heat of water is twice that of ice. When equilibrium is reached, the calorimeter will contain

A water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure), tr e wat'r from the cooler is used to cool an external device that generates constantly $3 \mathrm{~kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ} \mathrm{C}$ and the e.tire stored $120$ litres of water is initially cooled to $10^{\circ} \mathrm{C}$. The entire system is thermally insulat $\mathrm{d}$. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is

(Specific heat of water is $4.2 \mathrm{~kJ}^{-1} \mathrm{~kg}^{-1}$ and the density of water is $10.$) $0 \mathrm{k}^2 \mathrm{~m}^{-3}$ )