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).

Ice in a freezer is at $-7^{\circ} C .100 \,g$ of this ice is mixed with $200 \,g$ of water at $15^{\circ} C$. Take the freezing temperature of water to be $0^{\circ} C$, the specific heat of ice equal to $2.2 \,J / g { }^{\circ} C$, specific heat of water equal to $4.2 \,J / g ^{\circ} C$ and the latent heat of ice equal to $335 \,J / g$. Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to .......... $g$

$0.1\,m^3$ of water at $80\,^oC$ is mixed with $0.3\,m^3$ of water at $60\,^oC$. The final temperature of the mixture is ........ $^oC$

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 $35\,^oC$ ?

In an experiment a sphere of aluminium of mass $0.20\, kg$ is heated upto $150\,^oC$. Immediately, it is put into water of volume $150\, cc$ at $27\,^oC$ kept in a calorimeter of water equivalent to $0.025\, kg$. Final temperature of the system is $40\,^oC$. The specific heat of aluminium is ............ $J/kg\,-\,^oC$ (take $4.2\, Joule= 1\, calorie$)

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