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

A block of ice with mass $m$ falls into a lake. After impact, a mass of ice $m/5$ melts. Both the block of ice and the lake have a temperature of $^o C$. If $L$ represents the heat of fusion, the minimum distance the ice fell before striking the surface is

An unknown metal of mass $192\, g$ heated to a temperature of $100\,^oC$ was immersed into a brass calorimeter of mass $128\, g$ containing $240\, g$ of water at a temperature of $8.4\,^oC$. Calculate the specific heat of the unknown metal if water temperature stabilizes at $21.5\,^oC$. (Specific heat of brass is $394\, J\, kg^{-1}\, K^{-1}$) ……… $J\, kg^{-1}\, K^{-1}$

Compared to a burn due to water at $100°C$, a burn due to steam at $100°C$ is

$150 \,g$ of ice is mixed with $100 \,g$ of water at temperature $80^{\circ} C$. The latent heat of ice is $80 cal / g$ and the specific heat of water is $1 cal / g ^{\circ} C$. Assuming no heat loss to the environment, the amount of ice which does not melt is ……….. $g$