$A$ gun fires a lead bullet of temperature $300 \ K$ into a wooden block. The bullet having a melting temperature of $600 \ K$ penetrates into the block and melts down. If the total heat required for the process is $625 \ J$,then the mass of the bullet is . . . . . . grams. (Latent heat of fusion of lead $= 2.5 \times 10^4 \ J \ kg^{-1}$ and specific heat capacity of lead $= 125 \ J \ kg^{-1} K^{-1}$)

$2 \ kg$ of ice at $-20^{\circ} C$ is mixed with $5 \ kg$ of water at $20^{\circ} C$. What is the final amount of water in the mixture (in $kg$)? (Given: specific heat of ice $= 0.5 \ cal/g^{\circ} C$,specific heat of water $= 1 \ cal/g^{\circ} C$,latent heat of fusion of ice $= 80 \ cal/g$)

An amount of ice of mass $10^{-3} \ kg$ and temperature $-10^{\circ} C$ is transformed to vapour of temperature $110^{\circ} C$ by applying heat. The total amount of heat required for this conversion is,(Take,specific heat of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$,specific heat of water $= 4180 \ J \ kg^{-1} \ K^{-1}$,specific heat of steam $= 1920 \ J \ kg^{-1} \ K^{-1}$,Latent heat of ice $= 3.35 \times 10^5 \ J \ kg^{-1}$ and Latent heat of steam $= 2.25 \times 10^6 \ J \ kg^{-1}$) (in $J$)

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?

$A$ lead ball moving with a velocity $V$ strikes a wall and stops. If $50\%$ of its energy is converted into heat,then what will be the increase in temperature? (Specific heat of lead is $S$)

$A$ $10.0 \,W$ 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 ................ $\times 10^3 \,J K^{-1} kg^{-1}$.