# Thermodynamics Entropy question

## 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?

## 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?

Mapes
Homework Helper
Gold Member
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 sorta 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?

Mapes
Homework Helper
Gold Member
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?

Mapes