Question

A gas mixture contains monoatomic and diatomic molecules of 2 moles each. The mixture has a total internal energy of (symbols have usual meanings)

• A. 3 RT
• B. 5 RT
• C. 8 RT
• D. 9 RT

Answer 1

The Correct Option is C

The internal energy of a monatomic gas is given by $U_\text{mono} = \frac{3}{2}nRT$, and the internal energy of a diatomic gas is given by $U_\text{di} = \frac{5}{2}nRT$, where:

• $n$ is the number of moles,
• $R$ is the universal gas constant, and
• $T$ is the absolute temperature.

We are given a mixture containing 2 moles each of monatomic and diatomic molecules. Thus, $n_\text{mono} = n_\text{di} = 2$. The total internal energy of the mixture is the sum of the internal energies of the individual gases:

$U_\text{total} = U_\text{mono} + U_\text{di}$

$U_\text{total} = \frac{3}{2}n_\text{mono}RT + \frac{5}{2}n_\text{di}RT$

$U_\text{total} = \frac{3}{2}(2)RT + \frac{5}{2}(2)RT$

$U_\text{total} = 3RT + 5RT$

$U_\text{total} = 8RT$

The correct answer is (C) 8 RT.