Interesting problem (not homework)

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Discussion Overview

The discussion revolves around a thermodynamic problem involving the phase changes of ice in a vacuum chamber. Participants explore the heat required to convert 1 kg of ice at -10 degrees Celsius into vapor at 100 degrees Celsius, considering the implications of sublimation and pressure conditions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant poses a problem about heating ice in a vacuum chamber, noting the complexities introduced by sublimation and the work done by vapor against pressure.
  • Another participant asserts that achieving the desired state is impossible, referencing the pressure conditions for water vapor at 100 degrees Celsius and its position on the phase diagram.
  • A subsequent reply suggests reducing the mass of ice to 0.6 kg to achieve nearly 1 atmosphere of pressure for the resulting vapor.
  • Another participant refines this further, proposing that 0.58835 grams would be more appropriate, indicating that this amount would prevent the water vapor from behaving as an ideal gas and suggesting a specific path along the phase diagram.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of the original problem, with some suggesting adjustments to the mass of ice while others maintain that the conditions cannot be met as initially stated. The discussion remains unresolved regarding the exact parameters for achieving the desired phase change.

Contextual Notes

Participants highlight the dependence on the phase diagram of water and the implications of pressure on the behavior of water vapor, indicating that assumptions about ideal gas behavior may not hold in this scenario.

ideasrule
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Suppose I put 1 kg of -10-degree ice in a 1 m^3 vacuum chamber. How much heat do I have to add to turn all of the ice into vapor at 100 degrees Celsius?

This seems like a ridiculously simple problem, but I realized I've no idea how to solve it. First of all, ice sublimates in a vacuum, which complicates the problem a lot. Then there's the problem that when the water boils, the newly created gas has to do work against the existing pressure to expand. Any ideas?
 
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You can't. Think about what the pressure would be for 1 kg of water vapor occupying 1 cubic meter at 100 C. Then look at where that spot is on a water phase diagram.
 
Right, stupid me. What if there was 0.6 kg of ice? That would make the water vapor have almost exactly 1 atmosphere of pressure.
 
0.58835 grams would be better.

WIth this amount of water, this means the water vapor is not going to be an ideal gas. On the plus side, you can make it so the water vapor takes a jaunt along right along the gas edge of the phase diagram.
 

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