Thermodynamics

[IL Pre Med]

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Okay I'm not sure if I'm tweaking out but I think the answer to this question is wrong. Can someone double check?

One mol of helium is equilibrated at STP in a cylinder equipped with a moveable piston of negligible mass. After equilibration the piston is insulated, and a transformation is completed resulting in the temperature of the gas falling to –100˚C, with atmospheric pressure continually maintained. What is the final volume of the gas? Recall that the internal energy of a monatomic ideal gas is given as: E = (3/2)RT. (R = 0.08 L.atm/mol.K)


Correct Answer: 10.1 L

Explanation

One mol of helium is equilibrated at STP in a cylinder equipped with a moveable piston of negligible mass. After equilibration the piston is insulated, and a transformation is completed resulting in the temperature of the gas falling to –100˚C, with atmospheric pressure continually maintained. The final volume of the gas is 10.1 L.



Since the question tells us the piston is insulated (q = 0), we know all changes in E are because of pressure-volume work. So ΔE = –PΔV = 3/2 RΔT.



3/2 R(ΔT) = 3/2(0.08)(–100) = (3/2)(–8) = –12

–12 = –PΔV = 1 atm (ΔV)

ΔV = –12 L



And since 1 mol of an ideal gas at STP has 22.4 L of volume, the resultant volume is ~10.4 L, making 10.1 L the best answer.

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I put 22.4 and I believe that's correct. Why are they using (C) in the equation for temp? It should be 173 because the constant is in (K)

 

[monkeyvokes]

they are using C for the delta T value because it's just a change. A change of 100 is the same for the two scales.

 

[IL Pre Med]

they are using C for the delta T value because it's just a change. A change of 100 is the same for the two scales.

Ah you're right, thank you for the clarification. I was staring at it for so long and couldn't figure it out. Always good to have a fresh set of eyes take a look.

 

[monkeyvokes]

also, I believe you can solve this by using PV-nRT for conditions before and after, and then finding the volume difference.

 

[sps27]

I am a bit curious here but why nobody thought of using Charles law for this question. V1/T1 = V2/T2 (pressure being constant). V1=22.4 (1 mole at STP) T1=298, V2=? and T2=173. So you don't need R value etc.. Anyways, the answer is not close to 10.1 if you use Charles law but it is around 13 L.