Which of the following systems possesses the highest entropy?

A sugar crystal in a hot cup of coffee

A sugar cube in a hot cup of coffee

Powdered sugar in a hot cup of coffee

No sugar in a hot cup of coffee

Question

Which of the following systems possesses the highest entropy?
 	
	
A sugar crystal in a hot cup of coffee
	
A sugar cube in a hot cup of coffee
	
Powdered sugar in a hot cup of coffee
	
No sugar in a hot cup of coffee

aaronq · Answer

entropy:   solid<liquid<gas

anonymous · Answer

so would it be no sugar?

aaronq · Answer

no, i guess what i said is not that helpful in this situation. 

Since they all include a cup of hot coffee, we can ignore that and focus on the variables.

What is more ordered: a crystal, a cube, or powdered?

anonymous · Answer

crystal

aaronq · Answer

the crystal will have less imperfections then the cube, which will have many more.
That leaves us with powder, is powder less or more ordered than a sugar cube?

aaronq · Answer

than the cube*

anonymous · Answer

the powder is less ordered than the cube right? so the cube is the most ordered of them all

aaronq · Answer

correct, the powder is less ordered. Although i would argue that the crystal is more ordered because you have many crystals in the cube which won't be arranged as perfectly as the crystal. Even if the cube was a whole crystal, there would be more defects/impurities in a large crystal.

anonymous · Answer

ok so since the cube is more ordered than it increases entropy when placed in the hot coffee?

anonymous · Answer

I also have one more question! Is it true that entropy is the tendency of more concentrated energy to spread out into less concentrated forms or does it not depend on concentration?

aaronq · Answer

the cube less ordered than the crystal.

anonymous · Answer

ok so the crystal increases the entropy

aaronq · Answer

a more disordered state leads to a positive entropic value. So a more ordered state decreases entropy.

and yes, entropy is a measure of the degree of spreading and sharing of thermal energy
within a system.

anonymous · Answer

ok so the most unordered sugar (the powdered) increases entropy opposed to the most ordered (crystal) which would decrease the entropy

aaronq · Answer

yes, exactly.

anonymous · Answer

ok thanks! and the other statement about the concentration is true as well

aaronq · Answer

no problem, dude. and yes, it's true.