# Entropy of Ice-Water: Solving the Puzzle

• anubis01
In summary, the problem involves a 1.30×10-2 Kg cube of ice at an initial temperature of -12.0 C being placed in 0.470 Kg of water at 50.0 C in an insulated container. The final temperature is found to be 46.98 C. The calculation of entropy involves adding up all the stages where the ice melts and the water warms up to the final temperature, using the specific heat of water for the liquid water stage.
anubis01

## Homework Statement

A 1.30×10-2 Kg cube of ice at an initial temperature of -12.0 C is placed in 0.470 Kg of water at 50.0 C in an insulated container of negligible mass.

mi=1.3x10-2 Kg
mw=0.470 Kg
Ti=-12 C
Tw=50 C
ci=2100
cw=4190
Lf=3.34*10^5

Qi=Qw
S=Q/T

## The Attempt at a Solution

okay so first I tried to find Tf
Qi=Qw
mi(Lf+ci(Tf-Ti))=mwcw(Tw-Tf)
1.3x10-2(3.34*105+2100(Tf+12))=0.47*4190(50-Tf)
27.3Tf+327.6+4342=-1969.3Tf+98465
Tf=46.98

for entropy I tried to add up all the stages where ice->0 C + ice->water + ice water->Tf + hot water->Tf

S=[miciln(T2/Ti)]+[miLf/T]+[micw ln(Tf/T)]+mwcw ln(Tf/Tw)
S=[1.3x10-2*2100ln(273.15/261.15)]+[(1.3x10-2*3.34x105/273.15)]+[1.3x10-2*4190 ln(46.98+273.15/273.15)]+[0.470*4190 ln(46.98+273.15/50+273.15)]
=1.2264+15.896+8.644-18.490=7.28

I still get the wrong answer when using this method so if someone could point me in the right direction that would be much appreciated.

But once the ice melts, the H2O (at 0 C) then warms up to the final temperature as liquid water, not ice. So you have to use the specific heat of water for that stage.

AM

oh I get it now, thanks for the help.

## 1. What is entropy and how does it relate to ice-water?

Entropy is a measure of the disorder or randomness in a system. In the case of ice-water, it refers to the amount of energy required to convert the ordered structure of ice into the more disordered structure of liquid water.

## 2. Why is the entropy of ice-water considered a puzzle?

The entropy of ice-water is considered a puzzle because it seems to violate the second law of thermodynamics, which states that the entropy of a closed system will always increase over time. However, the entropy of ice is actually lower than that of liquid water, which goes against this law.

## 3. How is the puzzle of ice-water entropy solved?

The puzzle is solved by considering the entire system, including the surroundings, rather than just the ice and water. When the energy required to melt the ice is taken into account, the total entropy of the system does in fact increase, as predicted by the second law of thermodynamics.

## 4. What is the significance of understanding the entropy of ice-water?

Understanding the entropy of ice-water is important in many fields, including chemistry, physics, and climate science. It helps us better understand the behavior of water, which is essential for life on Earth, and also has practical applications in fields such as refrigeration and energy production.

## 5. Are there any ongoing studies or debates about the entropy of ice-water?

Yes, there are ongoing studies and debates about the entropy of ice-water, particularly in the context of climate change and the melting of polar ice caps. Scientists are constantly working to improve our understanding of this complex system and its impact on the planet.

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