Question 680: Thermodynamics & KTG

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 $\mathrm{T}^{\mathrm{x}}$. The value of $x$ is

Accepted Answer

In an ideal gas at temperature $ T $, the average force that a molecule exerts on the walls of a closed container is related to $ T $ raised to the power of $ x $. Let's determine the value of $ x $.
The pressure exerted by an ideal gas in a container can be expressed as follows:
$ 	ext{PV} = 	ext{NK}_{	ext{B}} T $
Where:
$ P $ is the pressure,
$ V $ is the volume,
$ N $ is the number of molecules,
$ K_{	ext{B}} $ is the Boltzmann constant,
$ T $ is the temperature.
Rearranging the formula for force $ F $, we get:
$ \frac{F}{A} \cdot V = NK_{	ext{B}} T $
Here, $ A $ is the area on which the force is applied. Solving for $ F $, we find:
$ F = \frac{NK_{	ext{B}} T A}{V} $
From this, it's clear that:
$ f \propto T $
Therefore, the exponent $ x $ is 1, indicating a direct proportionality between the force and the temperature.

Answer

0.25

Answer

2

Answer

0.5

Answer

1

Thermodynamics & KTG

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 \mathrm{T}^{\mathrm{x}}. The value of x is

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