Question

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

Answer 1

(a)

Law of conservation of Energy says that the energy is transferred from one body to another and from one format to another.
If we consider ideal conditions for heat transfer, when two bodies of temperature $T_1$ and $T_2$ come in thermal contact, heat transfer takes place from body of higher temperature to body of lower temperature.
The quantity thermal energy is the function of mass and temperature. Hence, the mean temperature of the bodies in contact will be given by the weighted average not normal average.
$\therefore T_{avg}=\frac{m_1{T}_1+m_2{T}_2}{m_1+m_2}$
Hence only when $m_1=m_2$, then $T_{avg}=\frac{T_1+T_2}{2}$

(b)

A coolant is required to have high heat capacity so that its temperature does not change much during heat transfer. Due to this, the coolant is able to hold more heat and allows quicker temperature drop in the hot body.

(c)

As the car moves, temperature of the gas inside the tyre increases.

$PV=nRT$

Since volume is almost constant, air pressure increases.

(d)

Water has a very high value of specific heat capacity. Due to this, the temperature of the water bodies do not change easily. Hence, climate near a harbour town is moderate.

Sand has a very low value of specific heat capacity. Due to this, the temperature of the sand changes rapidly. Hence, climate of a desert is extreme.