Thermodynamics - maximalization of temperature

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SUMMARY

The discussion focuses on the thermodynamic principles involved in maximizing the temperature of a metal cube using two other cubes at different temperatures (300K and 100K). The participant attempts to apply the Carnot cycle to extract work from the temperature gradient but realizes the need for entropy considerations. Ultimately, it is concluded that the maximum achievable temperature for the third cube cannot exceed 300K due to the laws of energy conservation, as any manipulation would only lower the average temperature in the system.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically the Carnot cycle.
  • Knowledge of temperature gradients and their role in heat transfer.
  • Familiarity with the concept of entropy in thermodynamics.
  • Basic principles of energy conservation in closed systems.
NEXT STEPS
  • Study the Carnot cycle and its implications for heat engines.
  • Research the role of entropy in thermodynamic processes.
  • Explore the principles of heat pumps and their applications in thermodynamics.
  • Investigate the laws of thermodynamics, particularly the first and second laws.
USEFUL FOR

Students studying thermodynamics, educators teaching heat transfer concepts, and anyone interested in the practical applications of energy conservation in thermal systems.

lakmus
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Homework Statement


We have three metal cubes, the same material, same size. Two cubes
have temerature 300K, third 100K.

On what maximal temperature can
we heat the on of the cubes?

The Attempt at a Solution


If we want to get higher temperature than 300K we need to
use the gradient of temperatures two cubes to get some work,
which we can after use to heating the third cube. I tried to place
ideal heat machine, which work on base of carnot cycle between
the two cubes (one 300K other 100K) - but I just have two temperatures
and on wiki is written, that to work from carnot cycle I need entrpy too.
So I don't know how to continue.

Thanks for any help.
 
Last edited:
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Can you post the exact wording of the question? Does the question allow you to use a heat pump or are they just expecting you to apply conservation of energy?
 
I can use heat pump. If I understand well the energy conservation law, then
the maximal temperature is 300K, any other manipulation will just make
average (so maximal temperature in the system will be lower) of temperatures . . .
 

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