Entropy and Maximum work for two idential, finite sized bodies

In summary, two identical, finite sized bodies of constant volume and constant heat capacity are used to drive a heat engine. Heat is taken from the hot body at Th, work is done, and heat is ejected to the cold body at Tc. Both bodies end up at Tf. The change in entropy of the system is given by ΔS=nCv*ln(Th/Tc). The maximum amount of work that can be done is equal to the change in internal energy, which is calculated by subtracting the initial internal energy from the final internal energy for both bodies.
  • #1
J.Welder12
5
0
Two idential, finite sized bodies of constant volume and constant heat capacity are used to drive a heat engine- heat is taken from the hot (Th) body, work is done, and heat is ejected to the cold (Tc) body. Both bodies wind up at Tf

(a) What is the change in the entropy of the system?

(b) What is the maximum amount of work that can be done?


Relevant equations
U=CvT
Cv is not time dependent


(a) I got ΔS=nCv*ln(Th/Tc)
(b) No idea where to start, any help would be great!
 
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  • #2
Welcome to PF, J.Welder12! :smile:

For (a) you need to consider the 2 bodies separately and apply your formula ΔS=nCv*ln(T2/T1) to them.
This gives 2 contributions to ΔS.

For (b) you should calculate U for both bodies before and after.
The difference is the maximum amount of work that can be extracted.
 

Related to Entropy and Maximum work for two idential, finite sized bodies

1. What is entropy and how does it relate to maximum work for two identical, finite sized bodies?

Entropy is a measure of the disorder or randomness in a system. It is related to the maximum work that can be obtained from two identical, finite sized bodies through the Second Law of Thermodynamics.

2. How does the Second Law of Thermodynamics relate to entropy and maximum work?

The Second Law of Thermodynamics states that the entropy of a closed system will always increase over time. This means that the maximum work that can be obtained from two identical, finite sized bodies will decrease as the system becomes more disordered.

3. What is the formula for calculating maximum work for two identical, finite sized bodies?

The formula for calculating maximum work is Wmax = (ΔS)T, where ΔS is the change in entropy and T is the temperature of the system. This formula is derived from the Second Law of Thermodynamics.

4. Can the maximum work for two identical, finite sized bodies ever be negative?

No, the maximum work for two identical, finite sized bodies cannot be negative. This is because the Second Law of Thermodynamics states that the entropy of a closed system will always increase, meaning that the maximum work will always decrease but never become negative.

5. How does the size of the bodies and the temperature affect the maximum work that can be obtained?

The size of the bodies and the temperature both play a role in determining the maximum work that can be obtained. As the size of the bodies increases, the maximum work also increases. However, as the temperature decreases, the maximum work decreases. This is because lower temperatures result in lower entropy and therefore, less maximum work can be obtained.

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