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

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SUMMARY

The discussion focuses on calculating the difference in entropy between a cup of water and a cup of ice under two conditions: both at 0°C and ice at 0°C while water is at 20°C. Participants clarify that at 0°C, water is in equilibrium with ice, resulting in zero entropy difference. They emphasize the need to consider the latent heat involved in phase changes and the correct application of the equations for heat transfer (Q = cmΔT) and entropy (S = Q/T). The importance of using Kelvin for temperature to avoid division by zero errors is also highlighted.

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  • Understanding of thermodynamics concepts, specifically entropy and phase changes.
  • Familiarity with the equations for heat transfer (Q = cmΔT) and entropy (S = Q/T).
  • Knowledge of temperature scales and their implications in thermodynamic calculations.
  • Basic principles of energy conservation in thermal systems.
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  • Research the concept of latent heat and its effect on phase transitions.
  • Study the implications of temperature scales in thermodynamic equations.
  • Learn about the calculation of entropy changes in mixed-phase systems.
  • Explore advanced thermodynamic equations and their applications in real-world scenarios.
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erin88
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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:
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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.

The next issue to address:
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:

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