Calculating work heat, and efficiency given a TS diagram

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Discussion Overview

The discussion revolves around calculating work done, heat transfer, and efficiency in thermodynamic systems using Temperature vs. Entropy (T-S) diagrams. Participants explore the relationships between these quantities and the implications of cyclic processes in thermodynamics.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the area within a T-S diagram represents heat, and in a cyclic process, the relationship Q = W holds true since the change in internal energy (∆U) is zero.
  • There is a suggestion that the area inside a triangle on the T-S diagram corresponds to work (W) and heat (Q), but some participants express uncertainty about the documentation supporting this interpretation.
  • Participants discuss two equations for efficiency: e = 1 - (Qc/Qh) and e = W/Qh, questioning if both are applicable and whether Qh and Qc correspond to specific temperature states (T2 and T1).
  • One participant clarifies that a T-S diagram is indeed a plot of Temperature vs. Entropy, correcting an earlier confusion with pressure.
  • Another participant confirms that the equations for efficiency are valid under the context of the first law of thermodynamics and explains how to interpret areas under the curve in relation to heat transfer in a Carnot cycle.

Areas of Agreement / Disagreement

Participants generally agree on the relationships between work, heat, and efficiency in the context of T-S diagrams, but there are varying levels of certainty regarding the interpretation of areas and the application of equations. Some aspects remain unresolved, particularly concerning the documentation and definitions used.

Contextual Notes

Limitations include potential misunderstandings about the representation of areas in T-S diagrams and the specific conditions under which the discussed equations apply, particularly in relation to reversible processes and equilibrium states.

abobo37
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Homework Statement



Is it possible to calculate the work done heat transfer, and efficiency of an object in a thermodynamic system, given the Temperature vs Entropy graph?

Example:
b7FPPj6.png

Homework Equations



∆U=Q-W
∆S=dQ/T
e=1-(Qc/Qh)
e=W/Qh

The Attempt at a Solution



Since this is a T vs S diagram,i can understand how the product(area) will be heat.
Since it's a cyclic process, I can also understand how Q=W , since ∆U=0
Currently I'm thinking that the area inside the triangle will be W, which also corresponds to Q. However, I could barely find any documentation on this, which is why I wanted to confirm it.

As for efficiency, we are given two equations:
1-(Qc/Qh)
and
W/Qh
Would both of them be correct here, and would Qh and Qc be T2 and T1 respectively?

Thanks!
 
Last edited:
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abobo37 said:

Homework Statement



Is it possible to calculate the work done heat transfer, and efficiency of an object in a thermodynamic system, given the Temperature vs Pressure graph?

Example:
b7FPPj6.png

Homework Equations



∆U=Q-W
∆S=dQ/T
e=1-(Qc/Qh)
e=W/Qh

The Attempt at a Solution



Since this is a T vs S diagram,i can understand how the product(area) will be heat.
Since it's a cyclic process, I can also understand how Q=W , since ∆U=0
Currently I'm thinking that the area inside the triangle will be W, which also corresponds to Q. However, I could barely find any documentation on this, which is why I wanted to confirm it.

As for efficiency, we are given two equations:
1-(Qc/Qh)
and
W/Qh
Would both of them be correct here, and would Qh and Qc be T2 and T1 respectively?

Thanks!
Is a T-S diagram a plot of Temperature vs. Pressure?
 
SteamKing said:
Is a T-S diagram a plot of Temperature vs. Pressure?
I'm so sorry, I meant entropy. I will edit it! :D
 
abobo37 said:

Homework Statement


3. The Attempt at a Solution [/B]

Since this is a T vs S diagram,i can understand how the product(area) will be heat.
Since it's a cyclic process, I can also understand how Q=W , since ∆U=0
Currently I'm thinking that the area inside the triangle will be W, which also corresponds to Q. However, I could barely find any documentation on this, which is why I wanted to confirm it.

As for efficiency, we are given two equations:
1-(Qc/Qh)
and
W/Qh
Would both of them be correct here
Certainly, since these are both statements of the 1st law.
and would Qh and Qc be T2 and T1 respectively?
For a Carnot cyccle, yes. A T-S diagram is valid for reversible processes only since entropy is defined for equilibrium states only.
T-S diagrams are ideal for reading heats in a closed cycle:
Qh = positive area under curve (going from left to right)
Qc = negative area under curve (going from right to left)
So Qh - Qc per cycle = area within the closed curve, as you correctly state, and = W also. And e = 1 - (Qc/Qh).
 
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Thanks for confirming!
 

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