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.

(N/A) When two bodies at different temperatures $T_1$ and $T_2$ are brought into thermal contact,heat flows from the body at the higher temperature to the body at the lower temperature until thermal equilibrium is achieved. The final equilibrium temperature is equal to the mean temperature $(T_1 + T_2) / 2$ only if the heat capacities of both bodies are equal. If the heat capacities differ,the equilibrium temperature will be closer to the temperature of the body with the higher heat capacity.
$(b)$ $A$ coolant in a chemical or nuclear plant must have a high specific heat capacity. This is because a substance with a high specific heat can absorb a large amount of heat energy for a relatively small rise in temperature. This allows the coolant to effectively remove excess heat from the plant components without its own temperature rising to dangerous levels.
$(c)$ When a car is driven,the friction between the tyres and the road,along with the internal compression of air,increases the temperature of the air inside the tyre. According to Gay-Lussac's Law (or Charles' Law for a fixed volume),for a fixed mass of gas in a constant volume,the pressure is directly proportional to the absolute temperature. Thus,as the temperature increases,the air pressure inside the tyre increases.
$(d)$ $A$ harbour town is located near a large body of water,which has a high specific heat capacity. Water heats up and cools down much more slowly than land. Consequently,the water acts as a heat reservoir,moderating the temperature of the air in the harbour town. In contrast,desert sand has a low specific heat capacity,leading to rapid temperature fluctuations,resulting in a more extreme climate.