Thermodynamic cycle efficiency

  • #1
4
0

Homework Statement


n moles of gas, that follow van der Waals equation are to be employed as the auxiliary system in a circular cycle(parameterized using T_h and T_c as shown on the TS diagram. Calculate the efficiency of the cycle.
300px-Carnot_cycle_TS.png

Homework Equations


,
, Q = TdS

The Attempt at a Solution


Idea is simple. I just devide circle curve horizontally in two two curves. Using Q = TdS , by integration over the top curve i obtain Q_(in), by integrating over the bottom curve i obtain Q_(out). Then i easily get efficiency using equation above. The only problem is, that i don't know, how to calculate those integrals with only van der Waals equation of state initially given.
 

Attachments

Answers and Replies

  • #2
20,867
4,546
What is the equation for the area of an ellipse in terms of the semi major and semi minor axes?
 
  • #3
4
0
Sorry, I wasn't precise enough, it has to be a circle, not an ellipse. I put that diagram more for an illustrative purpose.
 
  • #4
20,867
4,546
Sorry, I wasn't precise enough, it has to be a circle, not an ellipse. I put that diagram more for an illustrative purpose.
How can it be a circle if the units are different? If you change the units of either T or S, the shape changes.
 
  • #5
4
0
Absolutely.
The task itself states, that we are given a cycle, which is represented as a circle on a T-S diagram, which is parameterized using T_h and T_c.
My main concern though is, how would i get an expression of T as a function of S...
 
  • #6
20,867
4,546
Absolutely.
The task itself states, that we are given a cycle, which is represented as a circle on a T-S diagram, which is parameterized using T_h and T_c.
My main concern though is, how would i get an expression of T as a function of S...
$$\left(\frac{T-\frac{(T_H+T_C)}{2}}{\frac{(T_H-T_C)}{2}}\right)^2+\left(\frac{S-\frac{(S_{max}+S_{min})}{2}}{\frac{(S_{max}-S_{min})}{2}}\right)^2=1$$
 
  • #7
20,867
4,546
Like I said, since T and S have different units, you can't represent the variation as a circle on a T-S diagram. What don't you understand about this?
 
  • #8
4
0
I do understand it now. Thank you :)
 
  • #9
20,867
4,546
I do understand it now. Thank you :)
So what do you get for the efficiency?
 

Related Threads on Thermodynamic cycle efficiency

  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
2K
Replies
11
Views
30K
Replies
1
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
17
Views
1K
Replies
5
Views
547
Top