Question on adiabatic expansion

AI Thread Summary
The discussion revolves around a problem involving the adiabatic expansion of an ideal gas, where the user is struggling to calculate the work done (W) and the change in internal energy (dEint) after determining the initial and final pressures and temperatures. The user initially misapplies the formula for work in an adiabatic process, thinking it is W = nRdT, which leads to incorrect results. Participants clarify that the correct approach involves using the relationship PV^γ = constant and integrating the differential work equation dW = PdV. The user acknowledges their confusion and fatigue, ultimately deciding to seek clarification from their teacher the next day.
tristan_fc
Messages
12
Reaction score
0
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. :)
 
Physics news on Phys.org
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 PV^\gamma= K

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
dW=kV^-^\gamma dV

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

PV^\gamma= k

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

Similar threads

Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
Replies
8
Views
2K
Adiabatic expansion with temperature-dependent gamma
Replies
1
Views
1K
Adiabatic expansion of a piston in a cylinder filled with ideal gas
Replies
19
Views
3K
Volume ratio in an adiabatic gas expansion
Replies
9
Views
2K
How Do You Solve Adiabatic Expansion Problems in Thermodynamics?
Replies
5
Views
3K
Solving for final temp of adiabatic ideal air expansion
Replies
12
Views
2K
Adiabatic expansion of an ideal gas
Replies
4
Views
3K
Isothermal, isobaric and adiabatic
Replies
6
Views
2K
Adiabatic Expansion of a Gas: Final Pressure-Volume Product Calculation
Replies
1
Views
2K
Adiabatic expansion against constant pressure
Replies
6
Views
10K

Hot Threads

Recent Insights

Back
Top