Thermodynamics Entropy question

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Homework Help Overview

The problem involves calculating the entropy change of a 10-kg block of copper when it is submerged in a large lake, with the copper initially at 100 degrees Celsius and the lake at 280 K. The discussion centers around the concepts of entropy change for both the copper and the universe.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the energy transfer and entropy change, with one participant attempting to integrate the heat capacity over temperature to find the change in entropy. Others question the validity of using a simple division of energy by temperature and suggest integrating the entropy equation instead.

Discussion Status

The discussion is active, with participants exploring different methods to calculate the entropy changes. Some guidance has been provided regarding the integration of the heat capacity, and there seems to be a productive exchange of ideas about how to approach the problem mathematically.

Contextual Notes

Participants note the assumption that the lake is infinite compared to the copper, which may affect the calculations. There is also mention of the heat capacity being provided in a specific form in the original poster's textbook, which may influence the approach taken.

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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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