Question

One might think that the internal energy of diatomic gases is given by Eint=5RT/2. Do diatomic gases near room temperature have more or less internal energy than that? Hint: Their internal energy includes the total energy added in raising the temperature from the boiling point (very low) to room temperature.

(a) More
(b) Less
(c) Equal
(d) None of these

Answer 1

Diatomic gases have more internal energy than Eint = 5RT/2 near room temperature due to the additional vibrational energy associated with increased degrees of freedom.

Step-by-step explanation:

Diatomic gases at room temperature have more internal energy than Eint = 5RT/2 suggests, because the internal energy of a diatomic gas includes not only translational and rotational energy, which are accounted for by the 5RT/2 term, but also vibrational energy.

Near room temperature, diatomic gases have some of their vibrational degrees of freedom excited, thus contributing additional internal energy.

According to quantum mechanics, diatomic gases have 5 degrees of freedom (3 translational and 2 rotational) at low temperatures, but as the temperature increases, the vibrational modes can also become excited, effectively increasing the number of degrees of freedom and thus the internal energy. Therefore, the correct answer to the question is (a) More.