"Change in Entropy for Iron/Aluminum Equilibrium

In summary, at equilibrium, the temperature of the iron metal was 319.9 K and the aluminum was 903.7 K. The entropy changed by 0.
  • #1
slicknick
2
0

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)([tex]\Delta[/tex]T)

and for a process involving a temperature change i think we use:
[tex]\Delta[/tex]S = [tex]\int[/tex]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!
 
Last edited:
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
Last edited:

FAQ: "Change in Entropy for Iron/Aluminum Equilibrium

1. What is the concept of "change in entropy"?

The concept of "change in entropy" refers to the measure of disorder or randomness in a system. In thermodynamics, it is a measure of the amount of energy in a system that is unavailable for work. It is denoted by the symbol ΔS and is typically measured in joules per kelvin (J/K).

2. How is entropy related to the equilibrium of iron and aluminum?

In the context of iron and aluminum equilibrium, entropy is a key factor in determining the direction of the reaction. When iron and aluminum are in equilibrium, the system has reached a state of maximum disorder, which is associated with a higher entropy. This means that the reaction will proceed in a direction that increases entropy, resulting in a shift towards the more disordered state.

3. What factors affect the change in entropy for iron and aluminum equilibrium?

Several factors can influence the change in entropy for iron and aluminum equilibrium, including temperature, pressure, and the nature of the reactants and products. Generally, an increase in temperature or pressure will result in a larger change in entropy. Additionally, the complexity of the molecules involved can also impact the change in entropy.

4. How can the change in entropy for iron and aluminum equilibrium be calculated?

The change in entropy for iron and aluminum equilibrium can be calculated using the equation ΔS = ΣS(products) - ΣS(reactants), where ΣS represents the sum of the individual entropies of the products and reactants. The entropies can be found in tables or calculated using thermodynamic principles.

5. Why is understanding the change in entropy important in studying iron and aluminum equilibrium?

Understanding the change in entropy for iron and aluminum equilibrium is important because it allows us to predict the direction of the reaction and determine the conditions under which the reaction is most favorable. It also provides insight into the thermodynamic stability of the system and can be used to optimize processes involving iron and aluminum reactions.

Similar threads

Change in Entropy When Mixing Water at Different Temperatures
Replies
5
Views
365
Thermal Conductivity Problem-- Two Reservoirs
Replies
9
Views
2K
Calculate Entropy Change for Process 1->3 in Au Block
Replies
2
Views
2K
Chemistry No heat exchange with the surroundings in an irreversible expansion of an ideal gas?
Replies
4
Views
525
Calculate change in entropy per minute.
Replies
4
Views
1K
I Focus Problem for Entropy Change in Irreversible Adiabatic Process
2
Replies
60
Views
5K
Problem on entropy change and specific heat capacity
Replies
4
Views
4K
B Change in entropy of reversible isothermal process
Replies
11
Views
1K
Change in temperature for a system with entropy change
Replies
4
Views
2K
Entropy increase in adiabatic irreversible compression
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top