Change in Entropy for an isolated system

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SUMMARY

The discussion centers on the principles of thermodynamics in isolated systems, specifically addressing the relationship between internal energy changes (ΔU) and entropy changes (ΔS). It is established that in an isolated system, the total change in internal energy (ΔU_A + ΔU_B) equals zero, confirming that no heat exchange occurs with the surroundings. The final temperature (T_final) is derived using the formula T_final = (CA T_A + CB T_B)/(CA + CB), leading to the entropy change equation ΔS_final = CA*ln(T_f/T_A) + CB*ln(T_f/T_B). The conclusion affirms that in an isolated system, ΔU=0, indicating no work or heat exchange with the environment.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically internal energy and entropy.
  • Familiarity with the laws of thermodynamics, particularly the concept of isolated systems.
  • Knowledge of mathematical functions such as logarithms and their application in thermodynamic equations.
  • Basic grasp of temperature scales and their significance in thermodynamic calculations.
NEXT STEPS
  • Study the First and Second Laws of Thermodynamics in detail.
  • Learn about the concept of entropy and its implications in various thermodynamic processes.
  • Explore the derivation and applications of the Carnot cycle in isolated systems.
  • Investigate the role of heat capacity (C_A and C_B) in energy transfer and temperature changes.
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Students and professionals in physics and engineering, particularly those focusing on thermodynamics, energy systems, and entropy analysis in isolated systems.

Pouyan
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Homework Statement
Two systems, A and B, have the total constant heating capacities CA and CB as well as the initial temperatures TA and TB. They are put in contact with each other so that heat can be exchanged in a slow process without heat exchange with the surroundings. In the final state, both systems have assumed the same temperature. Determine the total entropy change in this process and show that it is positive.
Relevant Equations
dQ=TdS
dU=CdT
ΔU_A + ΔU_B = 0 (Is this because of isolated system am I right?)

ΔU_A = CA * (T_final - T_A )
ΔU_B=CB * (T_final-T_B)

And because of a very slow process : S=ln(T)
T_final= (CA T_A + CB T_B)/(CA + CB)

ΔS_final = CA*ln(T_f/TA) + ln(T_f/TB) * CB

My QUESTION is :

When we say No heat exchange with the surroundings or isolated system, do we mean ΔU=0 ?
 
Physics news on Phys.org
Yes. Isolated means no work and no external heat exchange.
 

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