Question

N moles of diatomic gas in a cylinder is at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant, but n moles of the diatomic gas get converted into a monoatomic gas. What is the change in the total kinetic energy of the gas?

(a) Increased
(b) Decreased
(c) Unchanged
(d) Cannot be determined

Answer 1

The total kinetic energy of the gas remains unchanged when n moles of diatomic gas are converted to monatomic gas at a constant temperature.

Step-by-step explanation:

When n moles of diatomic gas is converted into a monatomic gas at a constant temperature T, the total kinetic energy of the gas remains unchanged. This is because the kinetic energy of a gas depends only on the temperature and the number of moles of gas, according to the equipartition theorem. Each molecule, whether diatomic or monatomic, contributes the same amount of kinetic energy as long as the temperature remains constant. In this case, you've stated that the temperature T is held constant, so the kinetic energy, which is related to temperature, does not change when the diatomic gas is converted into a monatomic gas.