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:
A) 0
B) 1/2NkT
C) 3/2NkT
D) 5/2NkT
E) 3NkT

Question

Quizplus · Accepted Answer

The internal energy of an ideal diatomic gas (ignoring vibrational modes) is given by $U = \frac{5}{2}NkT$, where $N$ is the number of molecules, $k$ is the Boltzmann constant, and $T$ is the temperature. Doubling the number of molecules to $2N$ without changing the temperature doubles the internal energy, resulting in an increase of $\frac{5}{2}NkT$.

An Ideal Gas of N Diatomic Molecules Has Temperature T