Question

When a gas is in thermal equilibrium, its molecules
(a) have the same average kinetic energy
(b) have different energies which remains constant
(c) have a certain constant energy
(d) do not collide with one another

Answer 1

Temperature of a gas molecule at a particular instant is directly proportional to the kinetic energy of that molecule. From this relation, we can arrive at the characteristic of gas molecules in thermal equilibrium. The concept can also be related to the Zeroth law of thermodynamics.
Formula used:
$K=\dfrac{3RT}{2{{N}_{A}}}$

Complete answer:
We know that kinetic energy of a gas molecule is given by
$K=\dfrac{3RT}{2{{N}_{A}}}$
where
$K$ is the kinetic energy of a gas molecule
$R$ is the gas constant
$T$ is then temperature of the gas molecule at a particular instant
${{N}_{A}}$ is the Avogadro number
Let this be equation 1.
From equation 1, it is clear that kinetic energy of a gas molecule at a particular instant is directly proportional to the temperature of the gas, at that instant.
Now, if a gas is said to be in thermal equilibrium, we know that the temperature throughout the gas molecules is the same. Since this identical temperature is directly proportional to the kinetic energy of each gas molecule, we can say that the gas is said to have the same average kinetic energy.

Therefore, from the above explanation, we can say that option (a) is the correct answer.

Additional information:
Option (b) is incorrect as it contradicts the above explanation. Option (c) is also incorrect because we have already come to the conclusion that kinetic energy of a gas molecule is directly proportional to its temperature at a particular instant. At the same time, option (d) is completely wrong since gas molecules are said to have kinetic energies, which promotes collision among them.

Note:
The temperature consistency of all the gas molecules in thermal equilibrium can also be related to the Zeroth law of thermodynamics. This law talks about the thermal equilibrium condition between two systems, which are already in thermal equilibrium with another thermodynamic system. Unlike a single thermodynamic system under thermal equilibrium, a heat permeable wall needs to be considered here.