Comparing Temperature and Kinetic Energy for He and O2

[jgens]

Homework Statement

If you have on mole of He atoms and one mole of O₂ and add the same amount of energy to both, which underges the greater change in temperature? In which case are the particles, on average, moving faster.

Homework Equations

N/A

The Attempt at a Solution

I reasoned that for the first problem He would undergo the greater change in temp. since it has fewer degrees of freedom and all the energy goes into random translational kinetic energy. For the second problem I reasoned that the He particles must be moving faster because the have more KE and are less massive than O₂ molecules. Would someone mind letting me know if my reasoning is correct? Thanks.

 

[Andrew Mason]

Homework Statement

If you have on mole of He atoms and one mole of O₂ and add the same amount of energy to both, which underges the greater change in temperature? In which case are the particles, on average, moving faster.

The Attempt at a Solution

I reasoned that for the first problem He would undergo the greater change in temp. since it has fewer degrees of freedom and all the energy goes into random translational kinetic energy. For the second problem I reasoned that the He particles must be moving faster because the have more KE and are less massive than O₂ molecules.

Right on both points if by "more KE" you mean "more translational KE". The O2 and He molecules each have the same amount of kinetic energy if the same amount of energy is added to each and if they are kept separate.

AM

 

[nlightner]

Your reasoning is correct. The first problem is an application of the equipartition theorem, which states that each degree of freedom in a molecule will have an equal share of the total energy. Since He has fewer degrees of freedom (3 translational and 0 rotational) compared to O2 (3 translational and 2 rotational), all the energy will go into increasing the translational kinetic energy for He, resulting in a greater change in temperature.

For the second problem, you are also correct in stating that the He particles, on average, will be moving faster due to their lower mass and higher kinetic energy. This is because the average speed of a particle is directly proportional to its kinetic energy, and inversely proportional to its mass. Since He has a lower mass and higher kinetic energy compared to O2, its particles will have a higher average speed.