An ideal gas of N diatomic molecules has temperature T. If the number of molecules is doubled without changing the temperature, the internal energy increases by:

Question

Quizplus · Accepted Answer

The internal energy of a diatomic gas is given by U = (5/2)NkT, where N is the number of molecules, k is the Boltzmann constant and T is the temperature. When the number of molecules is doubled, N becomes 2N. Substituting this in the equation for internal energy, we get:
U' = (5/2)(2N)kT = 5NkT
Therefore, the increase in internal energy is U' - U = 5NkT - (5/2)NkT = (5/2)NkT, which is option D.

An Ideal Gas of N Diatomic Molecules Has Temperature T