Question 753: Thermodynamics & KTG

Question

An insulated container contains a diatomic 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

In an insulated container containing a diatomic gas with molar mass 'm', moving at velocity 'V', if the container is stopped suddenly, the change in temperature can be calculated as follows:
Kinetic Energy (K.E.) of the Gas:
The kinetic energy of the gas is given by:
$    	ext{K.E.} = n \left( \frac{1}{2} m V^2 ight)    $
Internal Energy Change (ÃÂU):
When the container is stopped, the change in internal energy is expressed as:
$    \Delta U = n C_v \Delta T    $
For a diatomic gas, the specific heat capacity at constant volume is:
$    C_v = \frac{5}{2} R    $
Energy Conservation:
Since energy is conserved when the container is stopped, the change in internal energy equals the initial kinetic energy:
$    \Delta U = 	ext{K.E.}    $
Solving for Change in Temperature (ÃÂT):
Substituting the expressions from above, we have:
$    n \frac{5}{2} R \Delta T = n \left( \frac{1}{2} m V^2 ight)    $
Cancelling 'n' from both sides and solving for ÃÂT:
$    \Delta T = \frac{m V^2}{5 R}    $
This expression gives the change in temperature of the gas when the container is abruptly stopped.

Answer

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

Answer

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

Answer

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

Answer

$\frac{5 m V}{3 R}$

Thermodynamics & KTG

An insulated container contains a diatomic 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)

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