Calculating Max Work from Reversible Cooling of Liquid

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SUMMARY

The maximum work that can be done on the surroundings while cooling one mole of a liquid with a constant molar heat capacity of 132 J/mol K from 80°C to 25°C is calculated to be 601 J, despite the total heat released being 7260 J. This discrepancy arises from the limitations imposed by the second law of thermodynamics, which dictates that not all energy can be converted to work in a reversible process. The change in entropy for the cooling process is 22.3 J/K, which is crucial for determining the maximum work output.

PREREQUISITES
  • Understanding of thermodynamics principles, particularly the second law of thermodynamics.
  • Familiarity with the concept of reversible processes in thermodynamics.
  • Knowledge of heat capacity and its role in calculating heat transfer.
  • Basic proficiency in calculating entropy changes in thermodynamic systems.
NEXT STEPS
  • Study the Carnot engine efficiency and its implications for work extraction in thermodynamic processes.
  • Learn about the relationship between heat transfer and work in reversible and irreversible processes.
  • Explore the mathematical derivation of entropy changes in various thermodynamic scenarios.
  • Investigate practical applications of thermodynamic principles in engineering and physical sciences.
USEFUL FOR

Students of thermodynamics, engineers working with heat engines, and anyone interested in the principles of energy conversion and efficiency in physical systems.

phizzle86
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Homework Statement



One mole of a liquid with a constant molar heat capacity of 132 j/mol K is initially at a temp of 80 C. The heat capacity is independent of tempearture. Calculate the maximum work that could have been done onthe surroundings while cooling the liquid reversibly. The surroundings are at a temp of 25 C.


Homework Equations




Given: q= -7260 J , change in entropy= 22.3J/K for the cooling

Change entropy = (Cvdt)/T

The Attempt at a Solution



maximum work here is in a reversible process would be the total amount of heat that is released that has the potential to do work, so wouldnt' that b 7260 J? The answer provided is 601 J

thanks guys
 
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Welcome to PF, phizzle86! :smile:

Did you consider that you cannot extract the maximum of energy as work?
The best you can do in any heat related process is the efficiency of a Carnot engine and in this case you can't even build one.
In other words, you need to respect the second law of thermodynamics.
 

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