How Much Ice Melts to Lower Water Temperature from 24°C to 5°C?

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of how much ice must melt to lower the temperature of a specific volume of water from 24°C to 5°C. Participants explore the appropriate use of specific heat capacities and the energy transfer involved in the melting process.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the heat required to lower the water temperature and initially uses the specific heat of water, questioning whether to use the specific heat of ice instead.
  • Another participant asserts that the specific heat of ice should be used since it is the ice melting that absorbs heat energy.
  • A different viewpoint suggests that the water from the melted ice must also be heated from 0°C to 5°C, indicating a need for clarity on temperature changes involved.
  • One participant emphasizes that the energy required for the phase transition of ice comes from the water, which has already been cooled, and that the specific heat of water is relevant for the calculations.
  • Another participant challenges the use of the specific heat of ice, arguing that the initial temperature of the ice is not provided, complicating the calculations.

Areas of Agreement / Disagreement

Participants express differing opinions on whether to use the specific heat of ice or water in the calculations, indicating a lack of consensus on the correct approach to the problem.

Contextual Notes

There is uncertainty regarding the initial temperature of the ice and how it should be factored into the calculations. Participants also highlight the complexity of energy transfer during the phase change and the need for clarity on temperature changes.

blueskadoo42
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Homework Statement



How much ice (in grams) would have to melt to lower the temperature of 351 ml of water from 24 deg C to 5 deg C? (Assume the density of water is 1.0g/ml .)

Homework Equations



q=mc(deltaT)

The Attempt at a Solution



m=351 g c=4.18J/g*C deltaT=19deg C

q=27.88kJ

then heat of fusion = 6.02kJ/mol

take 27.88/6.02 = 4.631 mol * 18.02g/mol= 83.45 grams.



this is wrong. the only problem i see is where i used the specific heat of water instead of ice. spec heat of ice=2.09. should I use the spec heat of ice instead of water? thanks!
 
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Doesn't the water from the ice have to go from 0°C to 5°C?
 
You should definitely be using the spec heat of ice. It is the ice which is melting, so that is where the heat energy is going and thus where the heat capacity matters. Otherwise, your attempt at a solution looks good to me.

What is the answer supposed to be?
 
Bacat said:
You should definitely be using the spec heat of ice. It is the ice which is melting, so that is where the heat energy is going and thus where the heat capacity matters.

Huh? Specific heat capacity is used to calculate the required energy for a temperature change. The initial temperature of the ice isn't provided, so presumably we should take it to be 0°C. It doesn't change temperature, it just melts!
 
Mapes, in order for the ice to melt it needs to take heat from somewhere. That heat comes from the water. That's why putting ice in water cools the water (it is heating the ice). It's just thermodynamics.
 
OK, prove me wrong and write the equation that uses the specific heat of ice, 2.1 J g-1 °C-1. You're going to need to multiply it by a temperature to get energy (and that temperature isn't 5°C or 24°C, because ice doesn't exist at those temperatures). Make sure your units match.
 
The energy required to melt the ice (phase transition) comes from the water that we assume the ice is surrounded by (to avoid taking heat from the air, which would complicate things). So he calculated the amount of heat required to change the temperature of the water by 19 degrees (using heat capacity of water). This heat energy went into melting the ice (not raising the temperature of the ice, but as a phase change). By measuring how much the temperature changed in the water (got colder), and knowing the heat capacity and molar heat of fusion you should be able to calculate how much ice melted to effect that change.

So actually that makes my previous statement wrong. You do need to use the spec heat of water, because it is the water we have temperatures for. Hmm...
 

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