A drilling machine of $10\,KW$ power is used to drill a bore in a small aluminium block of mass $8\,kg.$ If $50\%$ of power is used up in heating the machine itself or lost to the surroundings then  …….. $^oC$  is the rise in temperature of the block in $2.5\,minutes$

[specific heat of aluminium $= 0.91\,J/g\,\,^oc$ ]

A $20 \,g$ bullet whose specific heat is $5000 \,J kg ^{\circ} C$ and moving at $2000 \,m / s$ plunges into a $1.0 \,kg$ block of wax whose specific heat is $3000 \,J kg ^{\circ} C$. Both bullet and wax are at $25^{\circ} C$ and assume that $(i)$ the bullet comes to rest in the wax and $(ii)$ all its kinetic energy goes into heating the wax. Thermal temperature of the wax $\left(\right.$ in $\left.^{\circ} C \right)$ is close to

Ice at $-20\,^oC$ is added to $50\,g$ of water at $40\,^oC.$ When the temperature of the mixture reaches $0\,^oC,$ it is found that $20\,g$ of ice is still unmelted. The amount of ice added to the water was close to ……..$g$ (Specific heat of water $= 4.2\,J/g/^oC)$ Heat of fusion of water at $0^oC = 334\,J/g$ )

Water of volume $2\, L$ in a closed container is heated with a coil of $1\,kW$. While water is heated, the container loses energy at a rate of $160\, J/s$ . In how much time will the temperature of water rise from $27\,^oC$ to $77\,^oC$ ? (Specific heat of water is $4.2\, kJ/kg$ and that of the container is negligible)

A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ grams is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \ \mathrm{gm}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is