Two ideal gases, each consisting of N monatomic molecules, are in thermal equilibrium with each other and equilibrium is maintained as the temperature is increased.A molecule of the first gas has mass m and a molecule of the second has mass 4m.The ratio of the internal energies E₄_m/E_m is: A)1/4 B)1/2 C)1 D)2 E)4

Question

Quizplus · Accepted Answer

Since the two gases are in thermal equilibrium, they must have the same temperature. Therefore, according to the equipartition theorem, the average kinetic energy of each molecule is (1/2)kT, where k is Boltzmann's constant. The internal energy of an ideal gas depends only on its temperature and is given by U = (3/2)NkT. Therefore, the ratio of internal energies can be written as: E_m/E₄ = ((3/2)N1kT)/( (3/2)N2kT) Canceling out the common factors of (3/2) and N, we get: E_m/E₄ = (kT)/(4kT) = 1/4 Therefore, the answer is (A) 1/4.

Two Ideal Gases, Each Consisting of N Monatomic Molecules, Are