$A$ kettle with $2\, L$ of water at $27\, ^oC$ is heated by a coil heater with a power of $1\, kW$. The heat is lost to the atmosphere at a constant rate of $160\, J/s$ when its lid is open. In how much time will the water be heated to $77\, ^oC$ (specific heat of water $= 4.2\, kJ/(kg \cdot K)$) with the lid open?

$37 \ g$ of ice at $0^{\circ} C$ is mixed with $74 \ g$ of water at $70^{\circ} C$. What is the resultant temperature (in $^{\circ} C$)? (Specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of ice $= 80 \ cal \ g^{-1}$)

$A$ coffee maker makes coffee by passing steam through a mixture of coffee powder,milk,and water. If the steam is mixed at the rate of $50 \, g/min$ in a mug containing $500 \, g$ of mixture,then it takes about $t_0$ seconds to make coffee at $70^{\circ} C$ when the initial temperature of the mixture is $25^{\circ} C$. The value of $t_0$ is close to .......... $s$ (ratio of latent heat of evaporation to specific heat of water is $540^{\circ} C$ and specific heat of the mixture can be taken to be the same as that of water).

$15 \text{ g}$ of ice at $0^{\circ}\text{C}$ is added to a vessel containing water at $40^{\circ}\text{C}$. The mass of water and water equivalent of the vessel is $60 \text{ g}$. Assuming that negligible heat is taken from the surroundings, the final temperature of the mixture will be $[L_{\text{ice}} = 80 \text{ cal/g}, S_{\text{water}} = 1 \text{ cal/g}]$ (in $^{\circ}\text{C}$)

$200 \, g$ of a solid ball at $20 \, ^oC$ is dropped into an equal amount of water at $80 \, ^oC$. The resulting temperature is $60 \, ^oC$. This means that the specific heat of the solid is

One kilogram of ice at $0^{\circ}C$ is mixed with one kilogram of water at $80^{\circ}C$. The final temperature of the mixture is ........ $^{\circ}C$. (Take: specific heat of water $= 4200 \ J \ kg^{-1} \ K^{-1}$,latent heat of ice $= 336 \ kJ \ kg^{-1}$)