Question

A container having some gas was kept on a moving train. The temperature of the gas in the container will
$\left( {\text{A}} \right)$ Increase slightly
$\left( {\text{B}} \right)$ Remain the same
$\left( {\text{C}} \right)$ Decrease
$\left( {\text{D}} \right)$ Become infinite

Answer 1

Hint:The measurement of the kinetic energy is the temperature of a gas molecule.
The kinetic energy depends upon the velocity. Hence we have to calculate the velocities of the gas molecules to find their kinetic energies.
The velocity of any object can be calculated in a center of mass frame of that object. In another frame, it does not affect anything.

Complete step by step answer:
The temperature of a gas is the measurement of the average kinetic energy of the molecules present in it. And we know that the kinetic energy of an object depends upon the velocity of the object as,
KE = $\dfrac{1}{2} m v^2$

Such as, in a hot gas the gas-molecules move faster than in cold gas. When the velocity increases the mass g remains the same but the kinetic energy and temperature increase.
But, the velocity of any object can be calculated in a center of mass frame of that object. In another frame, it does not affect the kinetic energy and temperature.
Let go through the options given for the above problem,

$\left( {\text{A}} \right)$ On a moving train, the temperature of the gas in the container will increase slightly - this does not happen because the gas is kept in a jar and the jar is on the train. So, for the gas train is another frame that is not related to it. So the velocity of the train does not affect the temperature of the gas.

$\left( {\text{B}} \right)$ On a moving train, the temperature of the gas in the container will remain the same – this is the right answer because according to the gas train is another frame that is not related to it. So the velocity of the train does not affect the temperature of the gas. hence, the temperature will remain the same.

$\left( {\text{C}} \right)$ On a moving train, the temperature of the gas in the container will decrease - this does not happen because the temperature of the gas will not change due to the velocity increase of the train.

$\left( {\text{D}} \right)$ On a moving train, the temperature of the gas in the container becomes infinite – this is also not the right answer as the temperature will remain constant.
Hence the correct option is $\left( {\text{B}} \right)$

Note:The average kinetic energy of a gas is directly proportional to the absolute temperature only.
Since the gas molecules of an ideal gas possess all velocities in all possible directions, whose vector sum is zero hence the average velocity of an ideal gas is zero.