Solution
The pressure exerted by a gas on a wall is the result of the change in momentum of the molecules colliding with the wall.
$$ \text{Force} = \frac{\Delta p}{\Delta t} $$
The gas is maintained at bulk temperature $T_0$. The walls are at temperature $T$.
- Case $P_3$ ($T > T_0$): The wall is hotter than the gas. When molecules strike the wall, they gain thermal energy and rebound with higher speed ($v’ > v$). The change in momentum ($mv’ – (-mv)$) is larger. Thus, Pressure is highest.
- Case $P_2$ ($T = T_0$): The wall is at equilibrium. Collisions are statistically elastic. Pressure is nominal.
- Case $P_1$ ($T < T_0$): The wall is colder than the gas. Molecules lose energy to the wall and rebound with lower speed ($v’ < v$). The change in momentum is smaller. Thus, Pressure is lowest.
Therefore, $P_3 > P_2 > P_1$, which can be written as:
Correct Option: (a) $P_1 < P_2 < P_3$