$A$ metal ball of mass $0.1 \, kg$ is heated up to $500 \, ^\circ C$ and dropped into a vessel of heat capacity $800 \, J K^{-1}$ containing $0.5 \, kg$ of water. The initial temperature of the water and the vessel is $30 \, ^\circ C$. The approximate percentage increment in the temperature of the water is ........ $\%$. [Specific heat capacities of water and metal are $4200 \, J kg^{-1} K^{-1}$ and $400 \, J kg^{-1} K^{-1}$ respectively.]

$A$ $10 \ W$ electric 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 rises by $3 \ K$ in $15 \ min$. The container is then emptied,dried,and filled with $2 \ kg$ of oil. The same heater now raises the temperature of the container-oil system by $2 \ K$ in $20 \ min$. Assuming that there is no heat loss in the process and the specific heat of water is $4200 \ J \ kg^{-1} \ K^{-1}$,the specific heat of oil in the same unit is equal to:

How many grams of ice at $0 \, ^\circ \text{C}$ will be melted by $1 \, \text{g}$ of steam at $100 \, ^\circ \text{C}$? (Latent heat of fusion of ice $L = 80 \, \text{cal/g}$ and latent heat of vaporization of water $L' = 540 \, \text{cal/g}$)

$540 \ g$ of ice at $0 \ ^\circ C$ is mixed with $540 \ g$ of water at $80 \ ^\circ C$. The final temperature of the mixture is

$A$ $2\,kg$ copper block is heated to $500^\circ C$ and then it is placed on a large block of ice at $0^\circ C$. If the specific heat capacity of copper is $400\, J/kg/ ^\circ C$ and latent heat of fusion of water is $3.5 \times 10^5\, J/kg$,the amount of ice that can melt is:

When $0.15 \; kg$ of ice at $0^{\circ} C$ is mixed with $0.30 \; kg$ of water at $50^{\circ} C$ in a container,the resulting temperature is $6.7^{\circ} C$. Calculate the latent heat of fusion of ice. (Given: $s_{\text{water}} = 4186 \; J \; kg^{-1} \; K^{-1}$)