Question

If a gas is allowed to expand at constant
temperature then
(1) Number of molecules of the gas decreases
(2) The kinetic energy of gas molecules remains the
same
(3) The kinetic energy of gas molecules
increases
(4) The kinetic energy of gas molecules
decreases​

Answer 1

If gas is allowed to expand at constant

If gas is allowed to expand at constant temperature then (2) The kinetic energy of gas molecules remains the same.

• According to the kinetic theory of gases, kinetic energy is only dependent on temperature.
• It is directly proportional to temperature.
• Molecules are small and are in constant random motion while colliding with the walls of the container.
• The formula for kinetic energy is 1/2mv². here, m is the mass of the object and v is the velocity.
• It is an elastic collision as there is no loss or gain of energy.

Answer 2

The ideal gas equation is $PV=nRT$

At constant temperature, and for a given mass of a gas, the pressure is inversely proportional to volume

$pv=constant$

Hence at the constant temperature, during expansion of gas, the pressure decreases. Hence, option (A) is correct.

The expression for the average kinetic energy is  

$=(3/2)kT$

Hence, at the constant temperature, the kinetic energy remains same. Thus duringthe  expansion of a gas ata  constant temperature, the kinetic energy of gas molecules remainsthe  same.

Hence, option (B) is correct and

option (C) is incorrect.

The number of molecules of gas is not affected by the expansion or compression of a gas.

Therefore, option D is correct.