$1\,kg$ of ice at $-10\,^oC$ is mixed with $4.4\, kg$ of water at $30\,^oC$. The final temperature of mixture is ........ $^oC$  (specific heat of ice is $2100\, J/kg/k$)

A heater supplying constant power $P$ watts is switched $ON$ at time $t=0 \,min$ to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid $T(t)$ at equal time intervals. A graph is plotted with $T(t)$ on the $Y$-axis versus $t$ on the $X$-axis. Assume that there is no heat loss to the surroundings during heating. Then,

A refrigerator converts $500\,g$ of water at $25\,^oC$ into ice at $-10\,^oC$ in $3\,hours\,40\,minutes$ . The quantity of heat removed per minute is  ........ $cal/\min$

(Sp. heat of water $1\,cal/gm$, Specific heat of ice $= 0.5\,cal/g\,^oC$ , letent heat of fusion $= 80\,cal/g$ )

Water of volume $2\, L$ in a closed container is heated with a coil of $1\,kW$. While water is heated, the container loses energy at a rate of $160\, J/s$ . In how much time will the temperature of water rise from $27\,^oC$ to $77\,^oC$ ? (Specific heat of water is $4.2\, kJ/kg$ and that of the container is negligible)

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).

Steam at $100°C$ is passed into $1.1\, kg$ of water contained in a calorimeter of water equivalent $0.02 \,kg$ at $15°C$ till the temperature of the calorimeter and its contents rises to $80°C.$ The mass of the steam condensed in $kg$ is