"Change in Entropy for Iron/Aluminum Equilibrium

[slicknick]

Homework Statement

A 10 gram block of iron metal (Sp=0.449 J/gK) at 400 K is placed in contact with a 20 gram block of aluminum (Sp=0.903 J/gK) at 300 K. Heat flows between the two until equilibrium is reached. Find the equilibrium temp and the change in entropy for the process.

Homework Equations

q=m(Sp)($$\Delta$$T)

and for a process involving a temperature change i think we use:
$$\Delta$$S = $$\int$$Cp*dT/T

The Attempt at a Solution

First of all I was able to find the final temperature by using the first equation. It should be = 319.9 K. Where I get confused is do I use the Sp in place of Cp and then integrate? The reason I don't think I am doing this right is because there is a problem almost identical to it in the book (except that the metals and masses are the same) and I can't even get close to a right answer. Also in the one in the book, it asks for the change in the entropy for the universe and says that it is a positive non-zero number. How can that be true if the system is isolated and even if it isn't isolated how could you calculate the entopy change for the surroundings? I've tried it every way I can think of. please help!

 

[Mindscrape]

So you know that T final is the same for the two, and you are given T initial. Because the two systems are connected, they are related almost by a Newton's 3rd law type of relation (that the heat lost of one is the heat gain of another).

In any case like this, you just have to make sure the units are what you want to report. If you used your cited equation they wouldn't work to simply replace Cp with Sp.

dS/dU=1/T, and there is no work done, so dS/dQ=1/T. dQ=mSp*dT in this case so... dS = mSp*dT/T.

 

[slicknick]

Oh yeah that's what I was doing. You also have to multiply by the mass in order to cancel the units of grams so that your units are J/K. I guess then that I just don't understand the question that was similar or that its answer is wrong.Thanks for your help.