In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed…

In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed container depends on T as $\mathrm{T}^{\mathrm{x}}$. The value of $x$ is
  1. 0.25
  2. 2
  3. 0.5
  4. 1

Solution

Pressure exerted by an ideal gas in a container is $\begin{array}{ll} & P V=N K_B T \\ & \frac{F}{A} \cdot V=N K_B T \\ & F=\frac{N K_B T A}{V} \\ \therefore \quad & f \propto T \\ \therefore \quad & x=1 \end{array}$

Asked in: MHT CET 2024 (15 May Shift 2)

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