The average force applied on the wall of a closed container depends as $\mathrm{T}^{\mathrm{X}}$ where T is…

The average force applied on the wall of a closed container depends as $\mathrm{T}^{\mathrm{X}}$ where T is the temperature of an ideal gas. The value of $x$ is
  1. 0.5
  2. 1
  3. 2
  4. 1.5

Solution

$\begin{aligned} & P=\frac{F}{A} \\ \therefore \quad & P \propto F...(i) \end{aligned}$
From ideal gas equation, $\mathrm{P}=\frac{\mathrm{nRT}}{\mathrm{~V}}$
When V remains constant, $P \propto T...(ii)$
From (i) and (ii) $\begin{aligned} & F \propto \mathrm{~T}^{\mathrm{x}} \\ \therefore \quad & \mathrm{x}=1 \end{aligned}$ :

Asked in: MHT CET 2024 (10 May Shift 1)

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