Q120 / 150 · MHT CET 2024 (10 May Shift 1) · Physics
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
- A0.5
- Correct answerB1
- C2
- D1.5
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) $\begin{aligned} & F \propto \mathrm{~T}^{\mathrm{x}} \\ \therefore \quad & \mathrm{x}=1 \end{aligned}$
From ideal gas equation, $\mathrm{P}=\frac{\mathrm{nRT}}{\mathrm{~V}}$
When V remains constant, $P \propto T...(ii)$
From (i) and (ii) $\begin{aligned} & F \propto \mathrm{~T}^{\mathrm{x}} \\ \therefore \quad & \mathrm{x}=1 \end{aligned}$
Hence, the correct answer is option: 'B'.