What Is the Connection Between Exergy Heat and Losses?

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SUMMARY

The discussion clarifies the relationship between exergy heat and losses, specifically through the formula (1-Ta/Tc)*Q, which represents the maximum work obtainable from a heat transfer process. Ta is the atmospheric temperature (cold reservoir) and Tc is the higher reservoir temperature. While this formula indicates the maximum work achievable, it also implies that higher Tc leads to increased heat losses to the atmosphere, as the Carnot efficiency (1-Ta/Tc) dictates the fraction of heat energy that can be converted into work. Thus, both statements regarding maximum work and losses are valid within the context of thermodynamic principles.

PREREQUISITES
  • Understanding of thermodynamic concepts, specifically exergy and Carnot efficiency.
  • Familiarity with heat transfer principles and the role of temperature reservoirs.
  • Basic knowledge of entropy and its implications in thermodynamic systems.
  • Mathematical proficiency to interpret and manipulate thermodynamic equations.
NEXT STEPS
  • Research the implications of Carnot efficiency in real-world thermodynamic systems.
  • Explore the concept of entropy changes in thermodynamic cycles.
  • Study the relationship between temperature gradients and heat transfer rates.
  • Investigate advanced exergy analysis techniques for optimizing thermal systems.
USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, and anyone involved in energy systems optimization will benefit from this discussion.

PHstud
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Hello !

I am having a bit of trouble understanding something about exergy.

On one hand, I read that (1-Ta/Tc)*Q (exergy heat) is the maximum work given a heat transfer and a reservoir's temperature.

But from the other hand, I read that this exact same (1-Ta/Tc)*Q represents losses. ( Which i can also understand, if Tc is high, then the losses to the atmosphere will be higher due to the higher Heat transfer).

Does the two affirmations are true ? How ?

Thank you !
 
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Ta represents the atmospheric temperature (cold reservoir) and Tc represents the higher reservoir temperature. The expression (1-Ta/Tc) is what is called the Carnot efficiency. It's value is between 0 and 1 and it represents the maximum fraction of the heat energy absorbed at the the higher temperature Tc that can be used to do work so the maximum work is as you have written it. It does in general give you an idea of the minimum loss you can expect given by Ta/Ta but your expression gives the maximum work not losses. If Tc is very high, you can expect to do more work since the engine can only lose heat to the cold reservoir(assumed to have constant Ta).

If you are interested, a full explanation (e.g. on wikipedia) requires considering the changes in entropy of the entire system.
 

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