How Does Energy Transfer Affect Entropy in a Water-Ice System?

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Homework Help Overview

The discussion revolves around a thermodynamic problem involving the transfer of energy between a water-ice system. Specifically, it examines the change in entropy when 100 J of energy is transferred from 5 kg of water at 60 degrees Celsius to 1 kg of ice at 0 degrees Celsius, with a focus on the implications of this energy transfer on the state of the ice and water.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the assumptions regarding the melting of ice and the implications of energy transfer. Questions arise about whether all the ice will melt with the given energy transfer and the correct application of entropy change equations.

Discussion Status

Some participants have pointed out potential issues with the original poster's calculations and assumptions, particularly regarding the melting of ice and the use of entropy equations. There is an ongoing exploration of the problem's setup, including the conditions of thermal contact and the effects of energy transfer on temperature changes.

Contextual Notes

There is ambiguity in the problem statement regarding the thermal interaction between the water and ice, specifically whether they are in direct contact or separated by a barrier. This uncertainty may affect the interpretation of the energy transfer and the resulting temperature changes.

Lisa Marie
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Homework Statement


5 kg of water at 60 degrees are put in contact with 1 kg of ice at 0 degrees and are thermally isolated from everything else. The latent heat of ice is 3.3x105 J/kg

What is the change of entropy of the universe when 100J of energy are transferred from the water to the ice

2. Homework Equations

Q=+/- mL
Q=mcΔT
ΔS=|Q|/Tc-|Q|/TH

The Attempt at a Solution


mcΔT+mL+mcΔT=0
(5)(4200)(Tf-60)+(1)(3.3×105)+2000(1)Tf=0

23000Tf=96000
Tf=41.74 C

ΔS=100/(41.74+273)-100/(273)=-0.0486

I'm not getting the right answer for this one. Help would be greatly appreciated!
 
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You're assuming that all the ice is going to melt.
Lisa Marie said:

Homework Statement


5 kg of water at 60 degrees are put in contact with 1 kg of ice at 0 degrees and are thermally isolated from everything else. The latent heat of ice is 3.3x105 J/kg

What is the change of entropy of the universe when 100J of energy are transferred from the water to the ice

2. Homework Equations

Q=+/- mL
Q=mcΔT
ΔS=|Q|/Tc-|Q|/TH

The Attempt at a Solution


mcΔT+mL+mcΔT=0
(5)(4200)(Tf-60)+(1)(3.3×105)+2000(1)Tf=0
What does the last term represent? I figure it has something to do with the ice, but I'm not sure.

This expression also assumes that all of the ice melts. Is this possible if only 100 J of energy is transferred from the warm water to the ice? Can you describe in words what's going to happen?

23000Tf=96000
Tf=41.74 C

ΔS=100/(41.74+273)-100/(273)=-0.0486

I'm not getting the right answer for this one. Help would be greatly appreciated!
 
Firstly you can not use the relation $$\Delta S= \Delta Q/T$$ to find out entropy change for water, because here T is changing. Instead you should use the general relation $$\Delta S= \int dQ/T$$ to find out the change in entropy. This process should work out.
 
There is a bit of ambiguity regarding this problem statement. It is not clear whether the water and ice are in intimate contact, or whether they are separated by a diathermal barrier, and that, once the 100 J are transferred, the diathermal barrier is removed and replaced by an insulation barrier. The version with the barriers is simpler to solve. If 100 J is removed from the 5 kg of water, how much does its temperature drop?

Chet
 

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