Give 70J as heat to a diatomic gas

[cardguy1000]

Hi guys, I'm trying to interpret this problem but am having difficulties.

"We give 70J as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase"

Does "The gas molecules rotate but do not oscillate" mean the volume does not change?

I'm assuming I'd use deltaU = deltaQ - deltaW, with deltaW being p*deltaV since constant pressure. If the deltaV were 0 then deltaQ=70J-0 therefore yielding the answer of 70J which does not feel very comfortable, being the same.

 

[Tide]

You can view the molecules as rigid rotors - they have two rotational degrees of freedom but the two atoms comprising a molecule are constrained to a fixed separation from each other.

HINT: Think equipartition of energy!

 

[wais]

Hello, I understand your confusion with this problem. Let me try to break it down for you.

First, we are giving 70J of heat to a diatomic gas. This means that the gas is absorbing energy in the form of heat.

Next, the gas expands at constant pressure. This means that the pressure stays constant during the expansion, and the gas is allowed to expand without any external resistance.

Now, the statement "the gas molecules rotate but do not oscillate" is referring to the type of motion of the gas molecules. Diatomic gases, such as oxygen or nitrogen, have both rotational and vibrational modes of motion. However, in this problem, we are told that the molecules only rotate and do not vibrate. This means that the volume of the gas does change during the expansion, as the molecules are rotating and occupying more space.

To find the change in internal energy, we can use the formula deltaU = deltaQ - deltaW, as you mentioned. However, we need to calculate the work done by the gas during the expansion. Since the pressure is constant, we can use the formula W = p*deltaV.

If we assume that the initial volume of the gas is V, then the final volume would be V+deltaV. Substituting this into our formula, we get W = p*(V+deltaV - V) = p*deltaV.

Therefore, deltaU = deltaQ - p*deltaV. Since deltaQ is given as 70J and we know that the gas expands, deltaV is a positive value. This means that the change in internal energy will also be a positive value, indicating an increase in internal energy.

I hope this helps clarify the problem for you. Let me know if you have any further questions.