Max Temp Equilibrium: Achieving Max w/ Bodies at TA & TB

In summary: The answer is when the two bodies are placed next to each other such that the final temperature is (TA+TB)/2.
  • #1
cygnus2
16
0
Consider the following problem: you are given two BODIES at temp TA and TB.Do you agree that the maximum possible work i can extract from them happens to be in the case when they are left with the equilibrium final temperature of sqrt(TA.TB). This minimizes the entropy and hence corresponds to the maximum possible work extractable from the system.this is consequently the minimum possible equilibrium temperature.
now, we I am interested in the case of how its possible to attain maximum possible equilibrium temperature and what is its value? I think it would be when the bodies are placed next to each other such that the final temperature is (TA+TB)/2. In this case the useful work done would be zero, being entirely wasted to increase entropy.
do you agree?
 
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  • #2
The equilibrium temperature will be when the two bodies are at the same temperature. Then the entropy of the two bodies will be maximal. The equilibrium temperature will be in between TA and TB. But the exact value depends on the masses and specific heath of both bodies. You will obtain the maximum temperature when the colder object is very small, but then, you won't obtain much work.
 
  • #3
lpfr said:
But the exact value depends on the masses and specific heath of both bodies. You will obtain the maximum temperature when the colder object is very small, but then, you won't obtain much work.

see, it is clearly stated that given that the specific heat is C, the answer is to be in terms of TA and TB. And yes when the entropy is maximal, the work is very less. If you plot entropy in terms of Teq, where Teq is the equilibrium temp, then u'll find it is monotonically increasing.

The question still remains, what is the maximal possible equilibrium temp, irrespective of the work done?
 

1. What is Max Temp Equilibrium?

Max Temp Equilibrium refers to the state in which two bodies, each at different temperatures (TA and TB), come into thermal contact and reach a maximum temperature that is the same for both bodies. This means that both bodies have achieved thermal equilibrium with each other.

2. How is Max Temp Equilibrium achieved?

Max Temp Equilibrium is achieved when the two bodies are in thermal contact, meaning they are in close proximity to each other and able to exchange heat. The bodies will continue to transfer heat between each other until their temperatures equalize and reach a maximum value.

3. What factors influence Max Temp Equilibrium?

The key factors that influence Max Temp Equilibrium are the initial temperatures of the two bodies, the thermal conductivity of the materials they are made of, and the surface area and volume of the bodies. The larger the temperature difference between the bodies, the faster they will reach equilibrium. Materials with higher thermal conductivity will reach equilibrium faster, and bodies with larger surface area and volume will take longer to reach equilibrium.

4. Can Max Temp Equilibrium be achieved with more than two bodies?

Yes, Max Temp Equilibrium can be achieved with any number of bodies in thermal contact with each other. In this case, the final temperature reached will be the average of all the initial temperatures of the bodies.

5. What are some real-world applications of Max Temp Equilibrium?

Max Temp Equilibrium is an important concept in thermodynamics and has many practical applications. For example, it is used in the design of heating and cooling systems to ensure that the temperature of a room or building reaches a desired value. It is also important in understanding how heat is transferred between objects in nature, such as in the Earth's atmosphere or in the human body.

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