Average Mechanical Energy of Atoms in an Ideal Monatomic Gas

What is the average mechanical energy of the atoms of an ideal monatomic gas at 251 K?

Final Answer: The average mechanical energy of the atoms of an ideal monatomic gas at 251 K is approximately 3/2 kT, where k is the Boltzmann constant and T is the temperature in kelvin.

Answer:

The average mechanical energy of the atoms of an ideal monatomic gas at 251 K is approximately 3/2 kT.

The average mechanical energy of the atoms in an ideal monatomic gas can be calculated using the equipartition theorem. This theorem states that each degree of freedom contributes (1/2)kT to the total energy, where k is the Boltzmann constant and T is the temperature in kelvin.

For a monatomic gas, there are three translational degrees of freedom (corresponding to motion in the x, y, and z directions) and no rotational or vibrational degrees of freedom. Therefore, the total mechanical energy is given by:

E = (3/2)kT

Where E is the mechanical energy, k is the Boltzmann constant (approximately 1.38 x 10^-23 J/K), and T is the temperature in kelvin.

In this case, the temperature is 251 K, so we can calculate the average mechanical energy as follows:

E = (3/2) * (1.38 x 10^-23 J/K) * 251 K ≈ 5.18 x 10^-21 J

Therefore, the average mechanical energy of the atoms of an ideal monatomic gas at 251 K is approximately 5.18 x 10^-21 joules.