When $100\,g$ of a liquid $A$ at $100\,^oC$ is added to $50\,g$ of a liquid $B$ at temperature $75\,^oC$, the temperature of the mixture becomes $90\,^oC$. The temperature of the mixture, if $100\,g$ of liquid $A$ at $100\,^oC$ is added to $50\,g$ of liquid $B$ at $50\,^oC$, will be ……..$^oC$

$200 \,g$ 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 $=0.5 \,cal g ^{-10} C ^{-1}$ )

Two tanks $A$ and $B$ contain water at $30\,^oC$ and $80\,^oC$ respectively. Calculate the amount of water that must be taken from each tank to prepare $40\,kg$ water at $50\,^oC$

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

The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal ^{-1}{ }^{\circ} C ^{-1}$ ), is ……… $g$