Calculating the change in entropy of an ideal gas under compression

  • #1
28
0

Homework Statement


Initial
pressure: 140kPa
Temperature: 25C or 298K
Volume: 0.14m^3

Final
Pressure:1.4MPa or 1400kPa

It uses index compression, n=1.25. So PV^1.25 = constant.

c_p = 1.041kJ/kg.K and c_v = 0.743 kJ/kg.K

Homework Equations


¥ = c_p/c_v
ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) [i think]

The Attempt at a Solution


I found ¥ to be 1.4012
PV^n = 12 therefore Vf = 0.0222

140*0.14^1.25=11.989
1400*Vf^1.25=11.989
Vf^1.25=11.989/1400
 

Answers and Replies

  • #3
28
0
So far your work looks OK. Where are you stuck?
hi,

So where do i use the Vf? I don't I use "ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) " as part two asks for the final temperature. So part one wants me to find the entropy, but i dont know how to do this.
 
  • #4
PeterDonis
Mentor
Insights Author
2020 Award
34,708
12,896
Are there any other equations that involve the entropy? For example, for the special case (which it seems would apply to your problem) where the gas does not exchange heat with the environment?
 
  • #5
21,277
4,725
I don't see any problem with solving for the final temperature first and then substituting for the delta S. Alternately, you can solve for the temperature ratio in terms of the volume ratio by combining the polytropic relationship with the ideal gas law:
##\Delta lnT-\Delta lnV=\Delta lnP##
##n\Delta ln V=-\Delta lnP##

Solve for ##\Delta lnV## and ##\Delta lnT## in terms of ##\Delta lnP##

Chet
 
Last edited:

Related Threads on Calculating the change in entropy of an ideal gas under compression

Replies
4
Views
2K
  • Last Post
Replies
3
Views
942
Replies
2
Views
1K
  • Last Post
Replies
1
Views
932
Replies
3
Views
674
  • Last Post
Replies
5
Views
816
  • Last Post
Replies
1
Views
729
D
  • Last Post
Replies
1
Views
3K
Top