A mass of $50\,g$ of water in a closed vessel, with surroundings at a constant temperature takes $2\, minutes$ to cool from $30\,^oC$ to $25\,^oC$. A mass of $100\,g$ of another liquid in an identical vessel with identical surroundings takes the same time to cool from $30\,^oC$ to $25\,^o C$. The specific heat of the liquid is ………. $kcal/kg$ (The water equivalent of the vessel is $30\,g$.)

A block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to a $3\, kg$ water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container

An earthen pitcher used in summer cools water in it essentially by evaporation of water from its porous surface. If a pitcher carries $4 \,kg$ of water and the rate of evaporation is $20$ g per hour, temperature of water in it decreases by $\Delta T$ in two hours. The value of $\Delta T$ is close to ……….. $^{\circ} C$ (ratio of latent of evaporation to specific heat of water is $540^{\circ} C$

A $10.0 \,W$ electrical heater is used to heat a container filled with $0.5 \,kg$ of water.It is found that the temperature of the water and the container rose by $3 \,K$ in $15 \,min$. The container is then emptied, dried and filled with $2 \,kg$ of an oil. It is now observed that the same heater raises the temperature of the container-oil system by $2 \,K$ in $20 \,min$. Assuming no other heat losses in any of the processes, the specific heat capacity of the oil is ……………. $ \times 10^3 \,JK ^{-1} kg ^{-1}$

sphere of $0.047 \;kg$ aluminium is placed for sufficient time in a vessel containing boiling water, so that the sphere is at $100\,^{\circ} C .$ It is then immediately transfered to $0.14 \;kg$ copper calorimeter containing $0.25\; kg$ water at $20\,^{\circ} C$. The temperature of water rises and attains a steady state at $23\,^{\circ} C$. Calculate the specific heat capacity of aluminium in $kJ\;kg^{-1} K^{-1}$