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)

In an industrial process $10\, kg$ of water per hour is to be heated from $20^o C$ to $80^o C$ . To do this steam at $200^o C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^o C$. How many kg of steam is required per hour. (Specific heat of steam $= 0.5\, cal/g^o C$, Latent heat of vaporisation $= 540 cal/g)$

A copper block of mass $5.0\, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (ઇન $kg$) that can melt? [Specific heat of copper: $0.39\, Jg ^{-1 \circ} C ^{-1}$ and latent heat of fusion of water : $335 \,J g ^{-1}$ ]

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.$

A mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

…….. $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.