$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. Final mass of water in vessel is ……….. $g$ (specific heat of ice $=0.5 \,cal g ^{-10} C ^{-1}$ )

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 $10.$) $0 \mathrm{k}^2 \mathrm{~m}^{-3}$ )

A copper block of mass $5.0\, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (ઇન $kg$) that can melt? [Specific heat of copper: $0.39\, Jg ^{-1 \circ} C ^{-1}$ and latent heat of fusion of water : $335 \,J g ^{-1}$ ]

A copper ball of mass $100\ gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100\ gm$, filled with $170\  gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^o C$. $T$ is given by……$^oC$ (Given : room temperature $= 30^o  C$, specific heat of copper $=$ $0.1$ $cal/gm^o C$)

Calorie is defined as the amount of heat required to raise temperature of $1g$ of water by $1°C$ and it is defined under which of the following conditions