Thermodynamics problem for gas expansion at constant-volume

1. Sep 7, 2014

wintermute++

1. The problem statement, all variables and given/known data
This is a paraphrase, since this is only part of a 3 part question.

A sample of 1.00 mol perfect gas molecules with $C_{p,m}=7/2*R$ and initial pressure of 1.00 atm undegoes constant-volume heating to twice its initial pressure. Find q, w, ΔU, and ΔH.

2. Relevant equations
$PV=nRT$
$\Delta U=nC_{p,m}ΔT$

3. The attempt at a solution

$p_{f}=2p_{i}$ so $Δp = 2p_{i}-p_{i}=p_{i}$

Since the volume is constant, $V_{i}=V_{f}$ which lends itself neatly to give

$\Delta T = \Delta pV / nR = p_{i}V_{i}/nR = T_{i}$

Sure, it's a neat solution but it's obviously not the correct one since I don't have the initial temperature. I've tried other ways but don't see how this is possible given the information supplied. Any help would be appreciated.

The books solution requires a temperature change of 298 K, if that helps.

Last edited: Sep 7, 2014
2. Sep 7, 2014

wintermute++

If someone could just tell me whether this is even possible with the given information I would be grateful. It's from the Atkin's P. Chem textbook, 9th Edition. A second reason to suspect that it's not is because the 8th Edition version of this problem was written as "undegoes constant-volume heating to twice its initial volume" which makes no sense at all. I think they changed volume to pressure and forgot to add the needed information to solve it.

If someone could just confirm it would put my mind at ease. Otherwise I'm left sitting here thinking I'm an idiot.

3. Sep 8, 2014

Staff: Mentor

It is not possible. You need to know the initial temperature or the initial volume.

Chet

4. Sep 8, 2014

wintermute++

Thanks Chester. I spent way too much time looking for a solution to this problem!

5. Sep 8, 2014

Staff: Mentor

BTW, your equation for ΔU is incorrect. That is the equation for ΔH.

Chet

6. Sep 8, 2014

wintermute++

Ah, you're right. That was a typo in haste, I have it down on paper as Cvm = Cpm-R. Thanks again. I've been finding many errors with this p. chem textbook, beginning to wonder why it's so highly recommended.