Question on adiabatic expansion

In summary, the conversation discusses a problem involving the expansion of an ideal gas adiabatically. The final pressure, initial temperature, and final temperature are given, and the goal is to find the values for Q, W, and ΔEint. The formula for work done in an adiabatic process is discussed and refined, and it is determined that k, a constant, can be substituted into the equation. The conversation also mentions a textbook proof and a similar problem with different numbers.
  • #1
tristan_fc
12
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. :)
 
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  • #2
Formula for work done in adiabatic process is wrong
 
  • #3
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...
 
  • #4
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
 
  • #5
eh... P from above what? P is not constant.
 
  • #6
Refining it
[tex] dW=kV^-^\gamma dV [/tex]

I hope u will got it now
 
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  • #7
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...
 
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  • #8
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:
  • #9
Oh duh. Sorry, I guess I was just really tired last night. ;) Anyway thanks for the help.
 

1. What is adiabatic expansion?

Adiabatic expansion is a thermodynamic process where a system expands without exchanging heat with its surroundings. This means that the temperature of the system remains constant during the expansion.

2. How does adiabatic expansion differ from isothermal expansion?

In isothermal expansion, the temperature of the system remains constant as well, but heat is allowed to flow in and out of the system to maintain the temperature. In adiabatic expansion, there is no heat transfer and the temperature changes due to the expansion or compression of the system.

3. What is the equation for adiabatic expansion?

The equation for adiabatic expansion is PV^γ = constant, where P is the pressure, V is the volume, and γ is the ratio of specific heats for the gas. This equation is known as the adiabatic equation of state.

4. What are some real-world examples of adiabatic expansion?

One example of adiabatic expansion is the expansion of compressed air in a tire as a car drives. Another example is the expansion of air in a balloon as it rises in the atmosphere. The expansion of gas in a steam engine is also an example of adiabatic expansion.

5. What are the applications of adiabatic expansion in science and engineering?

Adiabatic expansion is used in various fields, such as in thermodynamics, meteorology, and engineering. It is used in the design of engines, turbines, and compressors. It is also important in understanding weather patterns and the movement of air masses in meteorology.

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