Question 787: Thermodynamics & KTG

Question

An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with velocity ' $V$ '. If it is stopped suddenly, the change in temperature is ( $R=$ gas constant)

Accepted Answer

When the insulated container, which contains a monoatomic gas with molar mass ' $ m $ ', is suddenly stopped from moving at velocity ' $ V $ ', there is a change in temperature due to the conversion of kinetic energy into internal energy.
The loss in kinetic energy of the gas is:
$    \frac{1}{2}(	ext{mn}) V^2    $
where $ n $ is the number of moles of the gas.
For a monoatomic gas, the change in internal energy is given by:
$    \Delta \mathrm{U} = \frac{3}{2} \mathrm{nR} \Delta \mathrm{T}    $
The change in kinetic energy is entirely converted into internal energy, leading to:
$    \frac{3}{2} n R \Delta T = \frac{1}{2} m n V^2    $
Solving for the change in temperature, $ \Delta T $, we have:
$    \Delta T = \frac{m V^2}{3 R}    $
This equation shows the direct relationship between the change in temperature and the initial velocity of the container, illustrating how kinetic energy influences the internal energy and hence the temperature change in an ideal gaseous system.

Answer

$\frac{\mathrm{mV}^2}{5 \mathrm{R}}$

Answer

$\frac{\mathrm{mV}^2}{3 \mathrm{R}}$

Answer

$\frac{\mathrm{mV}^2}{7 \mathrm{R}}$

Answer

$\frac{m V^2}{9 R}$

Thermodynamics & KTG

An insulated container contains a monoatomic gas of molar mass ' m '. The container is moving with velocity ' V '. If it is stopped suddenly, the change in temperature is ( R= gas constant)

Choose the correct answer: