The thermo $e.m.f.$ produced in a thermocouple is given by the equation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference between the two junctions. The neutral temperature is ............. $^oC$.

$A$ 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]

$250\,g$ of water and an equal volume of alcohol of mass $200\,g$ are placed successively in the same calorimeter and cool from $60^{\circ}C$ to $55^{\circ}C$ in $130\,s$ and $67\,s$ respectively. If the water equivalent of the calorimeter is $10\,g$,then the specific heat of alcohol in $\text{cal/g}^{\circ}C$ is:

Explain why:
$(a)$ Two bodies at different temperatures $T_1$ and $T_2$,if brought in thermal contact,do not necessarily settle to the mean temperature $(T_1 + T_2) / 2$.
$(b)$ The coolant in a chemical or a nuclear plant (i.e.,the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.
$(c)$ Air pressure in a car tyre increases during driving.
$(d)$ The climate of a harbour town is more temperate than that of a town in a desert at the same latitude.

$A$ block of ice at $-12^{\circ} C$ is slowly heated and converted into steam at $100^{\circ} C$. Which of the following curves best represents the event?

$A$ thermally insulated vessel contains some water at $0^{\circ}C$. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given that the latent heat of vaporization of water at $0^{\circ}C = 21 \times 10^5 \text{ J/kg}$ and the latent heat of fusion of water $= 3.36 \times 10^5 \text{ J/kg}$. The maximum percentage amount of water that will be solidified in this manner will be ...... $\%$