The average force applied on the walls of a closed container depends on $\mathrm{T}^{\mathrm{x}}$ where…

The average force applied on the walls of a closed container depends on $\mathrm{T}^{\mathrm{x}}$ where $\mathrm{T}$ is the temperature of an ideal gas. The value of ' $x$ ' is
  1. $4$
  2. $3$
  3. $2$
  4. $1$

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 $\mathrm{V}$ remains constant, $\mathrm{P} \propto \mathrm{T}.... (ii)$ Comparing (i) and (ii) $\mathrm{F} \propto \mathrm{T}^{\mathrm{x}}$ $\therefore \quad x=1$

Asked in: MHT CET 2023 (10 May Shift 1)

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