Question

One cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information.

(a) The rms speeds of atoms in the two gases are the same.
(b) The average kinetic energies of atoms in the two gases are the same.
(c) The internal energies of 1 mole of gas in each cylinder are the same.
(d) The pressures in the two cylinders are the same.

Answer 1

Helium and krypton gases at the same temperature have different rms speeds because of their different molecular masses, but they share the same average kinetic energy. Statements about internal energy and pressure cannot be determined without more information. The correct options are a,b,c,d.

Step-by-step explanation:

When comparing the properties of helium gas and krypton gas at the same temperature, we can assess several physical characteristics based on the kinetic theory of gases.

1. The rms speeds of atoms in the two gases are the same: False. Heavier gases like krypton have slower rms speeds than lighter gases like helium at the same temperature.
2. The average kinetic energies of atoms in the two gases are the same: True. At a given temperature, all gases have the same average kinetic energy per molecule.
3. The internal energies of 1 mole of gas in each cylinder are the same: Impossible to determine without additional information about the type of the gases and their degrees of freedom.
4. The pressures in the two cylinders are the same: Impossible to determine without information on volume, amount of gas and whether the gases are ideal.

Gases consisting of lighter molecules, such as helium, will have a higher rms speed compared to heavier molecules, such as krypton, at the same temperature.

However, the average kinetic energy for both gases will be the same because it only depends on temperature. Internal energy and pressure comparisons require more information about the conditions and gas behavior. The correct options are a,b,c,d.