Question on adiabatic expansion

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Homework Help Overview

The discussion revolves around an adiabatic expansion problem involving an ideal gas. The original poster is tasked with calculating the work done, change in internal energy, and heat transfer for a gas expanding from a specific initial state to a final volume, while noting that the heat transfer (Q) is zero in an adiabatic process.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply a formula for work done in an adiabatic process but questions its correctness after receiving feedback. Participants discuss the appropriate formula and the relationship between pressure, volume, and the constant k in the context of adiabatic processes.

Discussion Status

Participants are actively exploring the correct approach to calculating work done during the adiabatic expansion. There is a back-and-forth regarding the proper formulas and concepts, with some participants providing clarifications and others expressing confusion about the variables involved.

Contextual Notes

The original poster mentions a deadline for the assignment, indicating a time constraint that may affect their ability to resolve the problem during the discussion. There is also a reference to a textbook that provides some theoretical background but lacks practical application guidance.

tristan_fc
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I've been struggling with this problem for an hour or so now, and can't seem to find the right answer. Perhaps someone here can help? I would be very grateful. ;)

Two moles of an ideal gas ( = 1.40) expands slowly and adiabatically from a pressure of 5.09 atm and a volume of 12.7 L to a final volume of 30.0 L.

I had to find this stuff first, and I know I have all of it right.

final pressure: 1.528
initial temp: 393.5K
final temp: 279

Find Q, W, dEint.

I know Q is 0, and I know that Work and change in internal Energy are the opposite of each other, but I can't seem to find the right value for them. I thought work = nRdT, which in this case is:

2*.08214*(393.5-279)=1902.9

However, that answer is wrong according to webassign. There is also a problem in my textbook that is the same, except with different numbers, and i tried that one and got it wrong too. Anyone know what I'm doing wrong? Your help is greatly appreciated. :)
 
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Formula for work done in adiabatic process is wrong
 
so what is the proper formula? The textbook goes through a proof of why PV^y is constanst, but doesn't really go any further from that... I'm guessing that's somehow incorperated into the formula...
 
Write the differential equation for for work done for gas
i.e
dW=PdV

Note [tex]PV^\gamma= K[/tex]

substitute P from above in workdone equation and calculate the work done by taking limits from V1 to v2
 
eh... P from above what? P is not constant.
 
Refining it
[tex]dW=kV^-^\gamma dV[/tex]

I hope u will got it now
 
Last edited:
Okay, I thought maybe that's what you meant, but I'm sorry I don't see what good that does if I don't know what k is. Maybe I'm just slow tonight as I only got about 4 hours of sleep last night and am rather tired... Sorry. [zz)]

Ah well, it was due at midnight. So I'll just ask my teacher how to do it tomorrow...
 
Last edited:
k is a constant which is given by

[tex]PV^\gamma= k[/tex]

[tex]P_iV_i^\gamma = P_fV_f^\gamma= k[/tex]
 
Last edited:
Oh duh. Sorry, I guess I was just really tired last night. ;) Anyway thanks for the help.
 

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