Final answer:
The correct statements regarding root mean square speed (Urms) and average translational kinetic energy (Eav) of a molecule in a gas at equilibrium are that Eav at a given temperature is independent of molecular mass, Eav is doubled when temperature is increased fourfold, and Urms is inversely proportional to the square root of the molecular mass.
The correct options are A, C, and D.
Step-by-step explanation:
We need to determine which statement(s) about root mean square speed (Urms) and average translational kinetic energy (Eav) of a molecule in a gas at equilibrium are correct. Considering the provided information, let's analyze each statement:
A: Eav at a given temperature does not depend on the molecular mass of the gas. This statement is correct. The average kinetic energy of molecules in a gas at a given temperature is the same regardless of the molecular mass.
B: Urms is doubled when its temperature is increased four times. This statement is incorrect; the relationship is not directly proportional but rather square root proportional.
C: Eav is doubled when its temperature is increased four times. This statement is correct because average kinetic energy is directly proportional to the temperature.
D: Urms is inversely proportional to the square root of the molecular mass of the gas. This statement is correct. The heavier the molecule, the slower its root mean square speed at a given temperature.
The correct options are A, C, and D.