Question

The average force applied on the walls of a closed container depends as $\text{T}^\text{x}$ where T is the temperature of an ideal gas. The value of $x$ is

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Temperature is a measure of the average kinetic energy. Since $K.E. \propto T$ and $P \propto K.E.$, it follows that Force $\propto T$.

Answer 1

The Correct Option is A

Step 1: Concept
Pressure ($P$) is defined as force per unit area ($P = F/A$). For a container of fixed area, $F \propto P$.

Step 2: Meaning
According to the kinetic theory of gases, the pressure of an ideal gas is $P = \frac{1}{3} \rho v_{rms}^2$.

Step 3: Analysis
We know that the mean kinetic energy, and thus $v_{rms}^2$, is directly proportional to the absolute temperature $T$ ($v_{rms}^2 \propto T$). Therefore, $P \propto T$, which means $F \propto T^1$.

Step 4: Conclusion
The value of $x$ is 1. Final Answer: (A)