Question

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 $T^q$. A good estimate for $q$ is :

• A. $\frac{1}{4}$
• B. $1$
• C. $\frac{1}{2}$
• D. $2$

Answer 1

Answer: (B)

$1$

Given : 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 $T^q$. A good estimate for $q$ is :

Solution :

We have formula for pressure as $P=\frac{1}{3}\frac{MN}{V}{V}_{rms}^2$

or $P=\frac{\left(MN\right)T}{V}$

So we can write $P\propto V_{rms}^2\propto T$

so $Force\propto V_{rms}^2\propto T$

Hence Value of $q=1$

The Correct Option = B