2 body engine, final equilibrium temperate and work produced

In summary, two bodies with constant heat capacity C and 2C, initially at temperatures T and 2T, are connected by a reversible Carnot cycle heat engine. The final temperature of the bodies is equal to the equilibrium temperature T*. The change in entropy of the working fluid is zero, which means the total entropy change of the two reservoirs is also zero. Therefore, the final temperature is the average of the initial temperatures (T and 2T), and no work is performed by the heat engine.
  • #1
mrmerchant786

Homework Statement


2 bodies with contant heat capacity C and 2C, are initially at temp T and 2T. if a heat engine executing a reversible carnot cycle operates between the two bodies until their temperatures are equal, what is the final temp of the bodies and how much work is preformed by the heat engine

Homework Equations


W=Qη dQ=CdT

The Attempt at a Solution


q2 = C2 * (Tf-T2)
q1 = C1 * (Tf-T1)
So far this is where I'm at, I don't know how to proceed further to find the equilibrium temperature and then to fine the work produced
 
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  • #2
Suppose T* is the final temperature. In terms of T*, what is the change in entropy of each of the two reservoirs. Since you are operating using a Carnot cycle, the change in entropy of the working fluid is equal to zero. What does that tell you about the total of the entropy changes of the two reservoirs?
 
  • #3
Chestermiller said:
Suppose T* is the final temperature. In terms of T*, what is the change in entropy of each of the two reservoirs. Since you are operating using a Carnot cycle, the change in entropy of the working fluid is equal to zero. What does that tell you about the total of the entropy changes of the two reservoirs?

will it be zero?
so s1 +s2 = 0
 
  • #4
mrmerchant786 said:
will it be zero?
so s1 +s2 = 0
Yes. ##\Delta S_1+\Delta S_2=0##
 
  • #5
So, have you solved it yet?
 

1. What is a 2 body engine?

A 2 body engine is a type of heat engine that consists of two bodies at different temperatures, one acting as a heat source and the other as a heat sink. The difference in temperature between the two bodies creates a temperature gradient, which the engine uses to convert heat into work.

2. How is final equilibrium temperature determined in a 2 body engine?

The final equilibrium temperature in a 2 body engine is determined by the amount of heat transferred between the two bodies and their respective heat capacities. This temperature is reached when the two bodies reach thermal equilibrium, meaning they have the same temperature.

3. What factors affect the work produced by a 2 body engine?

The work produced by a 2 body engine is affected by the temperature difference between the two bodies, the heat transfer rate, and the efficiency of the engine. A larger temperature difference and higher heat transfer rate generally result in more work being produced, while a more efficient engine can convert more heat into work.

4. Can a 2 body engine operate at 100% efficiency?

No, it is impossible for a 2 body engine (or any heat engine) to operate at 100% efficiency. This is due to the second law of thermodynamics, which states that some heat will always be lost during the conversion process. However, the efficiency of a 2 body engine can be improved by reducing heat loss through insulation or increasing the temperature difference between the two bodies.

5. What are some real-world applications of 2 body engines?

2 body engines are commonly used in power plants to generate electricity. They can also be found in refrigerators, air conditioners, and heat pumps, where they use the temperature difference between the inside and outside of a building to transfer heat and cool or heat the space. Additionally, some car engines use the principle of a 2 body engine to convert heat from burning fuel into mechanical work to power the vehicle.

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