Question 709: Thermodynamics & KTG

Question

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

Accepted Answer

The average force applied on the wall of a closed container can be related to the temperature of an ideal gas using its dependency on temperature $ \mathrm{T}^{\mathrm{x}} $. To find the value of $ x $, we can derive it step by step:
The pressure $ P $ is defined as force $ F $ per unit area $ A $:
$    P = \frac{F}{A}    $
Therefore, pressure is proportional to force:
$    P \propto F \quad 	ext{.... (i)}    $
According to the ideal gas law, the pressure $ P $ is also given by:
$    P = \frac{nRT}{V}    $
where $ n $ is the number of moles, $ R $ is the ideal gas constant, $ T $ is the temperature, and $ V $ is the volume. If the volume $ V $ is constant:
$    P \propto T \quad 	ext{.... (ii)}    $
Combining equations (i) and (ii), we find the relationship between force and temperature:
$    F \propto T^x    $
From the proportionality derived:
$  x = 1  $

Answer

0.5

Answer

1

Answer

2

Answer

1.5

Thermodynamics & KTG

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

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