Supercooled Steam Homework: Solving for Tf, Condensation Fraction & ΔS

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Discussion Overview

The discussion revolves around a homework problem involving supercooled steam at 95˚C and its partial condensation into liquid water in a thermally-insulated vessel at constant pressure. Participants are tasked with determining the final temperature, the fraction of water that condenses, and the change in entropy for the process.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant notes the initial volume of steam and expresses uncertainty about how to proceed with finding the final temperature and volume.
  • Another participant suggests that the system will reach equilibrium at 100ºC, the boiling point of water, under constant pressure.
  • A participant emphasizes the need to equate the heat gained by the water to the heat lost by the steam, indicating that this relationship can help determine the moles of each substance involved.
  • One participant inquires about the heat released when steam condenses at 100ºC and asks for the heat of vaporization of water at that temperature.

Areas of Agreement / Disagreement

There is a general agreement that the final temperature will be 100ºC, but the exact calculations and reasoning behind the condensation fraction and change in entropy remain unresolved. Participants have differing levels of confidence in their understanding of the underlying physics.

Contextual Notes

Participants have not provided specific values for the heat of vaporization or other necessary constants, which may limit the ability to fully solve the problem. There is also a lack of consensus on the calculations needed to determine the fraction of water that condenses.

Who May Find This Useful

Students studying thermodynamics, particularly those interested in phase changes and heat transfer in gases and liquids.

Ariel Jo
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Homework Statement


You have 0.50 mol of steam which has been supercooled to 95˚C at 1 atm. Since the steam is below the boiling/condensation point, it proceeds to partially condense into liquid water. This happens in a thermally-insulated vessel at constant pressure.
(a) When the system re-attains equilibrium, what will the final temperature be?
(b) What fraction of the water will condense?
(c) Calculate ΔS for this process.

Homework Equations


ideal gas equation (the gas is assumed to behave ideally)
deltaS=n*Cp*ln(Tf/Ti)

The Attempt at a Solution


From PV=nRT, obtained an initial volume of steam of 15.1L but unsure how to proceed... Vf and Tf are both unknowns but should not be equal to Vi and Ti (from common sense - steam at 95degC will both condense and cool spontaneously.) Can easily find change in entropy from knowing final temperature... Would U=3/2RT be useful in this situation?
 
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Some hints:

Lacking other data, assume the water condenses until it reaches equilibrium.

Since the pressure is held constant, assume the volume is variable.

This seems to give a final temperature of 100º C. (The boiling point of water.)

So the basic question seems to be, how much water has to condense to heat the vapor back to 100º C.?
 
q(gained by water)=q(lost by steam), and at constant pressure this would be q=n*Cp*deltaT for both substances. Setting them equal to each other would give moles of each, but there are no calculations to get 100degC as the equilibrium temp, just the (seemingly sound, but I'm not a physics specialist) logic that for steam to not be supercooled it must be at 100degC or higher (when the pressure is a constant 1atm), if I understand you correctly.
Thanks for the help!
 
How much heat is given off (per mole) when steam condenses to liquid water at a constant temperature of 100 C? What is the heat of vaporization of water at 100 C?

Chet
 
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