• Support PF! Buy your school textbooks, materials and every day products Here!

Thermo: Need help finding T2 and V2 in an adiabat

  • Thread starter Courtknee
  • Start date
  • #1
2
0

Homework Statement



1 mole of ideal gas initially at 294 K is compressed adiabatically and
reversibly from 0.83 atm to 10.0 atm. Calculate the initial and …final volumes,
the final temperature, [itex]\Delta[/itex]U; [itex]\Delta[/itex]H; Q; and W: Assume that Cv = (5/2)R

Given:

n = 1 mol
T1 = 294 K
P1 = 0.83 atm
P2 = 10 atm
Q = 0

Find
V1, V2, [itex]\Delta[/itex]U, Q, [itex]\Delta[/itex]H, T2, W

Homework Equations



1. The professor gave that specific heat at constant volume is (5/2)R, however, the volume of the problem changes. Is this equation completely irrelevant to the problem?

2. How to you find the final temperature and final volume?


The Attempt at a Solution



I started off with PV = nRT for the initial givens and obtained that V1 = 29.1 L

Now, I'm stuck. I've tried using the ideal gas equation again, but I have 2 unknowns. I tried rearranging the equation and setting it equal the initial equations. I know how to find the other unknowns, but I'm stuck at this part for some reason.
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,586
346

Homework Statement



1 mole of ideal gas initially at 294 K is compressed adiabatically and
reversibly from 0.83 atm to 10.0 atm. Calculate the initial and …final volumes,
the final temperature, [itex]\Delta[/itex]U; [itex]\Delta[/itex]H; Q; and W: Assume that Cv = (5/2)R

Given:

n = 1 mol
T1 = 294 K
P1 = 0.83 atm
P2 = 10 atm
Q = 0

Find
V1, V2, [itex]\Delta[/itex]U, Q, [itex]\Delta[/itex]H, T2, W

Homework Equations



1. The professor gave that specific heat at constant volume is (5/2)R, however, the volume of the problem changes. Is this equation completely irrelevant to the problem?

2. How to you find the final temperature and final volume?


The Attempt at a Solution



I started off with PV = nRT for the initial givens and obtained that V1 = 29.1 L

Now, I'm stuck. I've tried using the ideal gas equation again, but I have 2 unknowns. I tried rearranging the equation and setting it equal the initial equations. I know how to find the other unknowns, but I'm stuck at this part for some reason.
You need to use the adiabatic condition: [itex]PV^\gamma = constant = K[/itex] which can be rewritten: [itex]TV^{\gamma-1} = K/nR = constant[/itex]

AM
 
  • #3
2
0
I'm assuming that the constant K will remain the same for p1*v1 and p2*v2

If I set P1V1γ = K, then I can use that constant for P2V2γ and obtain the volume, correct?
 
  • #4
Andrew Mason
Science Advisor
Homework Helper
7,586
346
I'm assuming that the constant K will remain the same for p1*v1 and p2*v2
If it didn't, it would not be constant!

If I set P1V1γ = K, then I can use that constant for P2V2γ and obtain the volume, correct?
Exactly.

AM
 

Related Threads on Thermo: Need help finding T2 and V2 in an adiabat

  • Last Post
Replies
2
Views
817
  • Last Post
Replies
2
Views
6K
Replies
6
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
6K
Replies
5
Views
2K
Replies
14
Views
8K
Top