# Entropy of Ice Cube vs Room Temp Water

• zeromodz
In summary, the conversation discussed the relationship between entropy and temperature, and how the addition of heat can affect both. It was mentioned that the equation s=q/t is not entirely accurate and that entropy is a measure of the number of possible distinct physical systems that satisfy certain conditions. It was also noted that entropy increases with temperature, but there are cases where temperature can remain constant while entropy increases, such as during a phase change.
zeromodz
Does an ice cube have more entropy than room temp water? I would intuitively think it doesn't because its atoms are more organized in a lattice vibrating like a solid. Conversely water would be more spread out and disorganized. However, the equation

s = q / t

states that the higher the temperature something has, the lower the entropy. So an ice cube would be colder than water making it have more entropy.

i think entropy us the measure of disorder an thus it increases when increasing temp and so also in this one the water has greater entropy than ice.

S is the CHANGE in entropy based on amount of heat added (Q) over the temp.

zeromodz said:
However, the equation

s = q / t

states that the higher the temperature something has, the lower the entropy.

Where did you see this equation? It isn't quite correct. Instead, $\Delta S=Q/T$ holds for reversible systems at constant temperature; that is, the addition of thermal energy Q causes a change in entropy $\Delta S$ for a system at temperature T.

The entropy of a system increases with temperature: $dS/dT=C/T$, where C is the heat capacity (which is positive for typical materials).

How can the temperature stay constant if your adding it taking heat away? Also is T the temperaute of the water you drop the ice cube in or the ice cube itself

The temperature isn't staying constant. It is simply the temp that the object was initially at before you added heat.

Also is T the temperaute of the water you drop the ice cube in or the ice cube itself

I believe it is both. You would use a separate equation for each one. In one you would have a Q and in the other you would have -Q. But I don't know for sure, that's just a guess.

To understand entropy you must understand that when we speak of "a system" with specific macroscopic state variables we really mean a class of systems. So the "system" in this case is somewhat of an abstraction. The entropy then is a measure of how broad one's definition of "the system" is. Entropy is the negative logarithm of the number (or measure in a continuum case) of --in principle-- empirically distinct physical systems satisfy the conditions for this class we call "the system".

This is why entropy is both "a measurement of our knowledge" and yet physically meaningful and hence calculable for laboratory systems.

So start with "the system" being the class of n water molecules contained within a fixed volume and having a fixed total energy. Pick a distribution for the velocities of each molecule. You can then count actual distinct cases this system class may represent and this gives you the entropy. Change the distribution and you get a different entropy. Observe that there is a distribution yielding maximum entropy (because it has the most distinct cases) and it will also be the most probable given no other information.

See how the entropy changes as one varies the total energy and you get the (reciprocal) temperature. Note that you can possibly have a negative temperature if e.g. increasing energy actually decreases entropy. There is also the in-between case where increasing energy increases entropy in a constant fashion, thus both go up while temperature is constant. This occurs e.g. during a phase change like when ice is melting.

dE = TdS

Now the equation you wrote: s = q/t when applicable would mean that for fixed energy q, as the entropy increases the temperature decreases, or that for fixed entropy as energy increases so does temperature, or for fixed temperature entropy increases with energy.

Your intuition about the water is correct since the (constant T) phase change as ice melts (since also T is positive) with dQ = TdS and since we observe the need to increase energy to melt the ice, we then know melting increases entropy as well.

## 1. What is entropy?

Entropy is a measure of the degree of disorder or randomness in a system. It is a thermodynamic quantity that describes the amount of energy that is unavailable for doing work.

## 2. How is entropy related to ice cubes and room temperature water?

The entropy of a system, such as an ice cube or room temperature water, increases as the system moves from a state of order to a state of disorder. In the case of an ice cube, the molecules are more ordered and have low entropy. As the ice cube melts and becomes water, the molecules become more disordered and the entropy increases.

## 3. What factors affect the entropy of an ice cube and room temperature water?

The main factor that affects the entropy of an ice cube and room temperature water is the temperature. As the temperature increases, the molecules move more rapidly and become more disordered, leading to an increase in entropy. Other factors that can affect entropy include pressure, volume, and the number of particles present in the system.

## 4. Why does an ice cube have lower entropy than room temperature water?

An ice cube has lower entropy than room temperature water because the molecules in an ice cube are more ordered and have less freedom of movement compared to the molecules in water. As the ice cube melts and becomes water, the molecules gain more freedom of movement and become more disordered, resulting in an increase in entropy.

## 5. Can entropy be reversed for an ice cube and room temperature water?

Yes, entropy can be reversed for an ice cube and room temperature water. This can occur through a process called reverse freezing, where the water molecules in room temperature water become more ordered and form an ice cube. However, this process requires energy to be input into the system, which is not feasible for everyday circumstances.

• Thermodynamics
Replies
1
Views
982
• Thermodynamics
Replies
19
Views
2K
• Thermodynamics
Replies
53
Views
2K
• Thermodynamics
Replies
4
Views
1K
• Thermodynamics
Replies
1
Views
816
• Introductory Physics Homework Help
Replies
10
Views
2K
• Thermodynamics
Replies
1
Views
845
• Thermodynamics
Replies
2
Views
1K
• Mechanics
Replies
5
Views
5K
• Biology and Chemistry Homework Help
Replies
1
Views
2K