Thermodynamics - Ideal gas expansion

  • Thread starter Chase11
  • Start date
  • #1
34
0

Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x


Homework Equations


ΔU=Q-W
W=[itex]\int[/itex]pdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=[itex]\int[/itex]pdV = nRT[itex]\int[/itex]dv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,621
363

Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x


Homework Equations


ΔU=Q-W
W=[itex]\int[/itex]pdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=[itex]\int[/itex]pdV = nRT[itex]\int[/itex]dv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
You are given Q. What is the relationship between Q and W if the process is isothermal?

AM
 
  • #3
34
0
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
 
  • #4
Andrew Mason
Science Advisor
Homework Helper
7,621
363
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
Express W in terms of n, T and Vi and Vf (check your equation for W - your integration is not correct). You have values for T, and Vf/Vi. If Q = W, express n in terms of Qm T, Vf/Vi

AM
 
  • Like
Likes 1 person

Related Threads on Thermodynamics - Ideal gas expansion

  • Last Post
Replies
6
Views
642
  • Last Post
Replies
2
Views
387
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
6
Views
6K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
1
Views
1K
Top