Entropy increase in dissipative systems

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SUMMARY

The discussion centers on the principles governing entropy increase in steady-state dissipative systems, specifically a mountain stream flowing at 1 liter per second with a 100-meter drop. The system exhibits a total energy of 980 watts, comprising both temperature rise and residual kinetic energy. Adding rocks to the flow increases temperature rise but reduces final kinetic energy, illustrating that the entropy increase can be minimized under specific constraints. The key principle is that maximizing kinetic energy leads to a lower entropy increase, challenging the notion that entropy should always be maximal within constraints.

PREREQUISITES
  • Understanding of thermodynamics and entropy concepts
  • Familiarity with steady-state systems and dissipative processes
  • Knowledge of energy conservation principles
  • Basic principles of fluid dynamics
NEXT STEPS
  • Research the Second Law of Thermodynamics in relation to dissipative systems
  • Explore the relationship between kinetic energy and thermal energy in fluid dynamics
  • Study the effects of constraints on energy dissipation in steady-state systems
  • Investigate practical applications of entropy management in engineering systems
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Physicists, engineers, and students studying thermodynamics, fluid dynamics, and energy systems will benefit from this discussion on entropy in dissipative systems.

Bob S
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Consider the following steady-state dissipative system. A mountain stream flowing 1 liter per second drops 100 meters over rocks and boulders, and at the bottom has both a temperature increase and a residual kinetic energy (velocity). The sum of the temperature rise and the kinetic energy is 980 watts. Maximum entropy increase would maximize the temperature rise, but because the stream has kinetic energy at the bottom, the temperature rise is not maximum. If I added rocks to the flow, the system constraints and the temperature rise would be higher. What is the over-riding principle that minimizes the entropy increase (maximizes the kinetic energy), based on the constraints of the system?
 
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In this steady state dissipative system, the additional constraint causes a larger heat dissipation and lower final state kinetic energy. The entropy increase is a minimum, subject to the constraints. I always thought that the entropy increase should be maximal, subject to the constraints. Which is correct?
Bob S
 
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