# Calculating work heat, and efficiency given a TS diagram

• abobo37
In summary, the conversation discusses the possibility of calculating work, heat transfer, and efficiency in a thermodynamic system using a Temperature vs Entropy graph. It is suggested that the area within the closed curve on the graph represents both heat and work, and that efficiency can be calculated using the equations 1-(Qc/Qh) and W/Qh. It is also mentioned that a T-S diagram is only valid for reversible processes, and that Qh and Qc correspond to T2 and T1 in a Carnot cycle.
abobo37

## 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:

∆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:
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:

∆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).

Chestermiller
Thanks for confirming!

## 1. What is a TS diagram?

A TS diagram, also known as a temperature-entropy or T-s diagram, is a graphical representation of a thermodynamic process in which temperature is plotted on the horizontal axis and entropy is plotted on the vertical axis.

## 2. How do you calculate work on a TS diagram?

The work done during a thermodynamic process can be calculated by finding the area under the curve on a TS diagram. This can be done by dividing the process into small segments and calculating the area of each segment, then adding them together.

## 3. How is heat calculated on a TS diagram?

Heat can be calculated by using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. On a TS diagram, the heat added or removed can be represented by the vertical distance between the curves.

## 4. What is efficiency on a TS diagram?

Efficiency on a TS diagram represents the ratio of the work output to the heat input during a thermodynamic process. It can be calculated by dividing the work done by the heat added to the system. A higher efficiency indicates that the system is able to convert a larger portion of the heat input into useful work.

## 5. Can efficiency be greater than 100% on a TS diagram?

No, efficiency cannot be greater than 100% on a TS diagram. This would violate the first and second laws of thermodynamics, which state that energy cannot be created or destroyed, and that the total entropy of a closed system will always increase over time.

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