Internal Energy of an Ideal Gas

[dropgigawatt]

Homework Statement

400. g of oxygen has a volume of .25 m³ and a pressure of 125,000 Pa. What is the internal energy of the gas? What would the internal energy of the gas be if it were compressed to .10 m³ while the pressure was held constant?

Homework Equations

U = 3/2 PV

The Attempt at a Solution

I got U = 3/2(125,000)(.25) = 46,875 J and when it is compressed it is 3/2(125,000)(.10) = 18,750 J. This seemed too easy and I did a quick web search and found that when it is compressing, the internal energy should increase. My solution shows a decrease in energy after the compression.

So I'm not sure what I'm supposed to do beyond just switching my value for volume (or why that wouldn't work)... can anyone help me out?

 

[voko]

Compressing ordinarily means an increase in pressure. In this case, pressure was held constant. That means it was not compressed, but something was done so that its volume decreased, while the pressure was kept. What could that be? How can one decrease the volume of gas without affecting its pressure?

 

[dropgigawatt]

Ah, lowering the temperature. So I take it I need to use V₁/T₁ = V₂/T₂ = nR and then U = 3/2nRT

Since I have 400 g of oxygen, n = 12.5 moles so I've got .25/T₁ = .10/T₂ = 103.875 but I don't know how to find the T values.

Am I on the wrong track?

 

[voko]

Why do you care about the temperature? U = (3/2) PV should work for any temperature, no?

 

[dropgigawatt]

That's what I originally tried. 3/2(125,000)(.10) = 18,750 J but that would mean it has more energy at a lower volume.

 

[voko]

I do not understand. At V = 0.25, U = 46,876 J. At V = 0.1, U = 18,750 J. How is 18,750 J more than 46,876 J?

 

[dropgigawatt]

I'm sorry, I misspoke. What I meant to say was after it is compressed, and the internal energy is 18,750 J, it is less than before, yes.

I didn't think that could be correct because in this thread (https://www.physicsforums.com/showthread.php?t=709788) the second post states that if the gas is compressed, the internal energy would increase. In that case, my answer wouldn't make sense, right?

 

[voko]

I addressed that concern in #2. You stated, correctly, that the temperature must decrease. What happens with internal energy when temperature decreases?

 

[dropgigawatt]

Oh! The internal energy must decease too! I totally misinterpreted what you were getting at in #2.

Thank you so much Voko.