Heat is being supplied at a constant rate to the sphere of ice which is melting at the rate of $0.1 \,gm / s$. It melts completely in $100 \,s$. The rate of rise of temperature thereafter will be ............ $^{\circ} C / s$

An earthen pitcher used in summer cools water in it essentially by evaporation of water from its porous surface. If a pitcher carries $4 \,kg$ of water and the rate of evaporation is $20$ g per hour, temperature of water in it decreases by $\Delta T$ in two hours. The value of $\Delta T$ is close to ........... $^{\circ} C$ (ratio of latent of evaporation to specific heat of water is $540^{\circ} C$

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)

The temperature of equal masses of three different liquids ${x}, {y}$ and ${z}$ are $10^{\circ} {C}, 20^{\circ} {C}$ and $30^{\circ} {C}$ respectively. The temperature of mixture when ${x}$ is mixed with ${y}$ is $16^{\circ} {C}$ and that when ${y}$ is mixed with $z$ is $26^{\circ} {C}$. The temperature of mixture when $x$ and $z$ are mixed will be ...... $^{\circ} {C}$

When $0.93\,watt-hour$ of energy is supplied to a block of ice weighing $10\,g,$ it is found that

Morning breakfast gives $5000 \,cal$ to a $60 \,kg$ person. The efficiency of person is $30 \%$. The height upto which the person can climb up by using energy obtained from breakfast is ......... $m$