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,the 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 heat of evaporation to specific heat of water is $540^{\circ} C$).

Two objects made of the same material have masses $m$ and $2m$ and are at temperatures $2T$ and $T$ respectively. When heat $Q$ is supplied to the object of mass $2m$, its temperature rises to $2T$. If the same heat $Q$ is supplied to the object of mass $m$, its temperature rises to:

$A$ mass $m$ of material exists in its solid state at its melting temperature $0^\circ C$. The following processes 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 amount of thermal energy $Q$ is added to the material, and the material is now a liquid at $40^\circ C$.
What is the ratio of the latent heat of fusion $(L)$ to the specific heat of the liquid $(s)$ for this material?

$A$ liquid at $30^{\circ} C$ is poured very slowly into a calorimeter at $110^{\circ} C$. The boiling point of the liquid is $80^{\circ} C$. It is observed that the first $5 \ gm$ of the liquid evaporates completely. After adding another $80 \ gm$ of the liquid,the equilibrium temperature is found to be $50^{\circ} C$. What is the ratio of the latent heat of the liquid to its specific heat? [Neglect heat exchange with the surroundings]

If the $emf$ of a thermocouple,one junction of which is kept at $0\,^{\circ}C$,is given by $e = at + 1/2\,bt^2$,then the neutral temperature will be

$A$ stationary object at $4^{\circ} C$ and weighing $3.5 \ kg$ falls from a height of $2000 \ m$ on a snow mountain at $0^{\circ} C$. If the temperature of the object just before hitting the snow is $0^{\circ} C$ and the object comes to rest immediately,then the quantity of ice that melts is (Acceleration due to gravity $= 10 \ m/s^2$,Latent heat of ice $= 3.5 \times 10^5 \ J/kg$)