Question

According to kinetic theory of gases, $0$ Kelvin is the temperature at which for an ideal gas.

Answer 1

Hint : To answer this question, we must know about the kinetic theory of gases and their energy and then we will be able to answer the question. After this we will be able to deal with all questions related to the energy of ideal gases.
For monatomic ideal gas:
${E_{\operatorname{int} }} = \dfrac{3}{2}NkT = \dfrac{3}{2}nRT$
Where,
${E_{\operatorname{int} }}$ is the total internal energy,
$N$ is the number of atoms in the gas,
$k$ is the Boltzmann's constant,
$R$ is the ideal gas constant and
$T$ is the temperature in kelvin.

Complete Step By Step Answer:
According to the question, the given temperature is $0$ kelvin, so let us put the value and see what we get the result,
$\because {E_{\operatorname{int} }} = \dfrac{3}{2}NkT \\\ \Rightarrow {E_{\operatorname{int} }} = \dfrac{3}{2}Nk \times 0 \\\ \Rightarrow {E_{\operatorname{int} }} = 0$
So, from the above result we can conclude that according to the kinetic theory of gases, the internal energy of an ideal gas is zero at $0$ kelvin.

Note :
Note that gases made up of molecules with more than one atom per molecule have more internal energy than $\dfrac{3}{2}nRT$ , because energy is associated with the bonds and the vibration of the molecules. Another interesting result involves the equipartition of energy, which says that each contributor to the internal energy contributes an equal amount of energy. For a monatomic ideal gas, each of the three directions (x, y, and z) contribute $\dfrac{1}{2}kT$ per molecule, for a total of $\dfrac{3}{2}kT$ per molecule.
For a diatomic molecule, the three translation direction contribute $\dfrac{1}{2}kT$ per molecule, and for each molecule there are also two axes of rotation, contributing rotational kinetic energy in the amount of $\dfrac{1}{2}kT$ each. This amounts to a total internal energy of ${E_{\operatorname{int} }} = \dfrac{5}{2}NkT = \dfrac{5}{2}nRT$ for a diatomic gas, and a polyatomic gas has contributions from three translation direction and three axes of rotation, giving ${E_{\operatorname{int} }} = 3NkT = 3nRT$ .