Question

A gas of temperature T is enclosed in a container whose walls are (initially) at temperature T₁.

• A. The gas exert a higher pressure on the walls of the container when T₁ < T.
• B. The gas exert a higher pressure on the walls of the container when T₁ > T.
• C. The gas exert same pressure in both cases.
• D. None of the above.

Answer 1

Answer: (C)

The gas exert same pressure in both cases.

Answer 2

For an ideal gas the pressure is given by

$$P=nkT \,,$$

where $n$ is the number density and $T$ is the temperature of the gas. In kinetic theory, the pressure results from the momentum transfer of gas molecules colliding with the container walls. Even if the wall temperature $T_1$ is different from the gas temperature $T$, the impulsive collisions of molecules coming from the bulk (which are characterized solely by $T$) remain unaltered. Although upon striking a diffusely reflecting wall the molecules re‐emit with a speed corresponding to $T_1$, the net pressure on the wall is determined by the properties of the gas (its actual Maxwellian distribution in the bulk) and is given by $nkT$. Thus, the pressure exerted by the gas remains the same regardless of whether $T_1<T$ or $T_1>T$.

Explanation (Minimal):

• Pressure $P=nkT$ depends only on gas parameters.
• Molecules from the bulk (at $T$) set the pressure via momentum transfer.
• Wall temperature $T_1$ affects re-emitted speeds but not the net pressure.