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 steam engine intakes $50\, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If latent heat of vaporization of steam is $540 \,cal g ^{-1}$, then the heat rejected by the steam engine per minute is .........$\times 10^{3}$$cal.$

$300\, gm$ of water at $25°C$ is added to $100\, gm$ of ice at $0°C$. The final temperature of the mixture is........ $^oC$

If mass energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

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

In a calorimeter of water equivalent $20 \,g$, water of mass $1.1 \,kg$ is taken at $288 \,K$ temperature. If steam at temperature $373 \,K$ is passed through it and temperature of water increases by $6.5^{\circ} C$ then the mass of steam condensed is ............ $g$