# Find the difference in entropy between a cup of water and a cup of ice

• erin88
In summary, the difference in entropy between a cup of water and a cup of ice is not 0 at T=0C due to the change in energy associated with melting/freezing. To find the change in entropy, the correct equation is Q=cmdeltaT, where T should be in units of temperature (K, C, F, R).
erin88
Find the difference in entropy between a cup of water and a cup of ice for each of these cases:
1. both are at T=0C
2. ice is at T=0C water is at 20C

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If the "water" is at 0C then it is ice right? and the difference in entropy is 0 correct?

For the second part... do you think I am supposed to find the Q for each one? since the equation for Q is Q=cmT I don't think this would make sense because the equation for entropy (S) is S=Q/T. For ice it would be 0/0 and you can't do that...

Do you think maybe he's asking for the change in entropy if you mix the two together?

Thanks.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EDIT

I just remembered the equation is Q=cmdeltaT

So this must mean that he does want to know the change of entropy in the system if you mix the two together??

Last edited:
erin88 said:
Find the difference in entropy between a cup of water and a cup of ice for each of these cases:
1. both are at T=0C
2. ice is at T=0C water is at 20C

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If the "water" is at 0C then it is ice right? and the difference in entropy is 0 correct?

For the second part... do you think I am supposed to find the Q for each one? since the equation for Q is Q=cmT I don't think this would make sense because the equation for entropy (S) is S=Q/T. For ice it would be 0/0 and you can't do that...

Do you think maybe he's asking for the change in entropy if you mix the two together?

Thanks.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EDIT

I just remembered the equation is Q=cmdeltaT

So this must mean that he does want to know the change of entropy in the system if you mix the two together??

First I'll address the conceptual problem:
Ice is not simply water at T=0C, there is change in energy associated with melting/freezing. I think this might give you a bit of a start on the first part.

We have $$Q = S T$$
The first question that crosses my mind is what are the units on T?
Should it be K? C? F? R? I think the answer to this question will relieve your divide by zero error.

Last edited:

Thanks.I would like to clarify the concepts of entropy and heat (Q) in this context. Entropy is a measure of the disorder or randomness in a system, while heat (Q) is a form of energy transfer between two objects due to a temperature difference.

In the first case, both the cup of water and cup of ice are at 0°C, meaning they both have the same temperature. However, the ice has a more ordered and less random molecular structure compared to the liquid water. This results in a higher entropy for the cup of water compared to the cup of ice. The difference in entropy between the two can be calculated by finding the change in entropy (ΔS) during the phase change from ice to water. This can be done by using the equation ΔS=Q/T, where Q is the heat absorbed during the phase change and T is the temperature at which the phase change occurs.

In the second case, the ice is at 0°C and the water is at 20°C. This means that the water has a higher temperature and thus a higher kinetic energy compared to the ice. When the two are mixed together, heat (Q) will transfer from the water to the ice until they reach a common temperature. This heat transfer will result in a change in entropy, as the molecules in the ice will become more randomly arranged and the water molecules will have a lower kinetic energy. The difference in entropy between the two can again be calculated using the equation ΔS=Q/T, where Q is the heat transferred and T is the final temperature reached by the system.

In summary, the difference in entropy between a cup of water and a cup of ice depends on the temperature and phase of the two substances. In both cases, there will be a change in entropy when the two are mixed together, but the specific values will depend on the temperature and heat transfer involved.

## 1. What is entropy?

Entropy is a thermodynamic quantity that measures the amount of disorder or randomness in a system. It is a measure of the number of possible microstates that a system can have.

## 2. How does entropy differ between a cup of water and a cup of ice?

The main difference in entropy between a cup of water and a cup of ice lies in the arrangement of molecules. In a cup of water, the molecules are constantly moving and have a higher degree of disorder, leading to a higher entropy. In a cup of ice, the molecules are arranged in a more ordered crystal lattice, resulting in a lower entropy.

## 3. What factors affect the difference in entropy between a cup of water and a cup of ice?

The main factors that affect the difference in entropy between a cup of water and a cup of ice are temperature, pressure, and the number of molecules present. Higher temperatures and pressures tend to increase entropy, while a larger number of molecules can lead to higher entropy due to more possible microstates.

## 4. Can the difference in entropy between a cup of water and a cup of ice be reversed?

Yes, the difference in entropy between a cup of water and a cup of ice can be reversed through a process called "melting." By adding energy (heat) to the cup of ice, the molecules become more disordered and the entropy increases, resulting in the formation of a cup of water.

## 5. How is the difference in entropy between a cup of water and a cup of ice relevant in everyday life?

The difference in entropy between a cup of water and a cup of ice is relevant in everyday life as it is a fundamental concept in understanding phase changes and heat transfer. For example, melting ice requires the input of energy, and this energy comes from the surrounding environment, causing a decrease in entropy in the environment. This concept also has applications in fields such as chemistry, biology, and engineering.

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