Work done on thermal systems confusion

In summary, the problem involves compressing an ideal gas in thermal isolation with a given curve on a p-v diagram. The initial volume and temperature are known, but the final volume and pressure need to be determined. The work done on the gas during compression is also to be calculated. After trying various equations and methods, one can use the equation PV^{\gamma}=C to solve for the final volume and pressure, and then use the work integral to calculate the work done.
  • #1
Ichiru
4
0
There is this seemingly simple problem I have but dispite everything I've tried to do I can't find a way to remove one of the unknown variables. Everytime I try to remove it with some other equation I end up figuring out that I don't know another one of the values and end up not being able to solve it. Then there is other information I really am not sure how it would help figure out the problem.

Original Problem:

An external force compresses 0.10 mol of an ideal gas in thermal isolation. The curve of this transformation on a p-v diagram is pV^1.4 = a constant. The gas initially has a volume of 1.6L and a tempature of 275K. When the compression is finished, the tempature has increased to 380K. (a) What are the final volume and final pressure? (b)How much work was done on the gas to compress it?


My attempt at the solution:

When I initially tried the problem I immediatly went to the section in my book that it was on and looked for any equations that would help me.

The only equation I found was that Work = integral of pdV from V1 to V2

My brain said, hey I can use that to find the work after I find the values!

So then I tried looking for problems to help me find what the final volume and pressure were so I could solve part b.

I ended up using the equation p = nRT/V to find the inital volume which I found to be 1.43atm. After that I tried putting the equation for p into the integral equation to try and solve it but realized I didn't know what work was so I couldn't solve it that way.

After that I tried searching my textbook for clues but as of yet found nothing.

Thank you for your time and any and all help is greatly appreciated
 
Physics news on Phys.org
  • #2
For isothermal expansion you have

[tex]PV^{\gamma}=C[/tex]

Which you can re-write as

[tex]P(V)V^{\gamma} = P_1 V_{1}^{\gamma}[/tex]

Solving for P(V) you get

[tex]P(V) = P_1 V_{1}^{\gamma}V^{-\gamma}[/tex]

Which makes the work integral

[tex]W = P_1 V_{1}^{\gamma}\int_{V1}^{V2}V^{-\gamma}dV[/tex]
 
  • #3
Thanks! I think I understand how to use that.
 

1. What is the definition of "work done" in thermal systems?

In thermal systems, work done refers to the energy transfer that occurs as a result of a change in temperature. This can be seen in processes such as heating, cooling, or phase changes.

2. How is work done on a thermal system calculated?

The work done on a thermal system can be calculated by multiplying the force applied to the system by the distance over which the force is applied. This is known as the work-energy theorem and is represented by the equation W = F x d.

3. What are some examples of work done on thermal systems?

Examples of work done on thermal systems include using a stove to heat food, using a refrigerator to cool drinks, and using a hair dryer to change the phase of water from liquid to gas.

4. How does work done on thermal systems affect the system itself?

The work done on a thermal system can cause changes in the system's internal energy, temperature, and phase. It can also result in changes in the system's surroundings, such as heating or cooling the surrounding environment.

5. Can work done on a thermal system be negative?

Yes, work done on a thermal system can be negative. This occurs when the system loses energy, such as when a gas expands and does work on its surroundings by pushing a piston, resulting in a decrease in the system's internal energy.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
867
  • Introductory Physics Homework Help
Replies
12
Views
849
Replies
10
Views
473
  • Introductory Physics Homework Help
2
Replies
56
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
637
  • Introductory Physics Homework Help
Replies
4
Views
614
  • Introductory Physics Homework Help
Replies
11
Views
3K
Back
Top