Thermodynamics Entropy question

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SUMMARY

The discussion focuses on calculating the entropy change of a 10-kg block of copper when it is submerged in a large lake at 280K. The entropy change of the universe is determined by considering both the system (the copper) and the surroundings (the lake). The user correctly identifies that the change in internal energy is equal to Q and suggests using the integral of the heat capacity of copper, C, from 373K to 280K to find the entropy change. The final approach involves integrating the equation dS = dQ/T, emphasizing the need to account for varying temperatures during the heat transfer process.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically entropy and heat transfer.
  • Familiarity with the concept of heat capacity and its integration.
  • Knowledge of the first law of thermodynamics and internal energy changes.
  • Ability to perform calculus operations, particularly integration.
NEXT STEPS
  • Study the derivation and application of the entropy formula dS = dQ/T.
  • Learn about temperature-dependent heat capacities and their implications in thermodynamic calculations.
  • Explore the concept of reversible and irreversible processes in thermodynamics.
  • Investigate the relationship between internal energy and entropy changes in different systems.
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Students studying thermodynamics, particularly those tackling entropy calculations, as well as educators and professionals in physics and engineering fields seeking to deepen their understanding of heat transfer and entropy changes in systems.

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Homework Statement



A 10-kg block of copper is initially 100 degrees celsius. It is thrown into a very large lake that is 280K. What is the entropy change of the piece of copper. What is the entropy change of the universe?

Homework Equations





The Attempt at a Solution


I know that the entropy change of the universe is the change of the system and the change of the surroundings. I Don't really know how to go about this problem. I know for say two copper blocks next to each other I can do ncdeltaT + ncdeltaT and b/c they have the same mass and C it is easy. however I'm assuming this won't work for a few reasons in this problem because the lake I'm pretty sure I am supposed to assume is infinite compared to the copper Can anyone help pleaseee?
 
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I think you need to think about the energy associated with heating the copper, and about finding the resulting entropy change by integrating an equation like q=T\,dS.
 
I worked out a solution let me see what you think(i was thinking something sort of like what you said)

I said change in internal = Q and changein internal is the integral from 373 to 280 of the C for copper which is 2.723/8.314(which is R) in my book dT (my book gives C's in Cp/R for some reason) Anyway after this integral is found I multiplied by 8.314 to get rid of the R then I said change in entropy for system is this value over 373 and for surr is the negative Q over 280 does this seem correct?
 
Just dividing the energy by 373 K isn't going to work for the copper; some of this energy is transferred when the copper is at 373 K, some at 303 K (for example), and some at 280 K. Try integrating the dS equation as I mentioned earlier.
 
so to get Q i do use the integral of C from 373 to 280 and then i take that and put it over T and do an integral from 373to 280 dT right?
 
Exactly. And if you assume that the heat capacity is temperature independent, the first integral is quite simple.
 
thanks a lot !
 

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