How to apply the Clausius-Clapeyron to geysers

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SUMMARY

The discussion focuses on applying the Clausius-Clapeyron relation to analyze geysers, specifically in a physics competition context. The user references a YouTube video for guidance but struggles to calculate the temperature at the bottom of the geyser using the provided values: P1 = 100,000 Pa, P2 = 113,000 Pa, and ΔHvap = 2.6 x 10^6 J/mol. The user initially misinterprets ΔHvap as the latent heat of vaporization instead of the change in enthalpy, which should be 41,000 J/mol. Correctly applying these values is essential for accurate temperature calculations.

PREREQUISITES
  • Understanding of the Clausius-Clapeyron relation
  • Familiarity with thermodynamic concepts such as latent heat and enthalpy
  • Basic knowledge of pressure and temperature relationships in gases
  • Proficiency in using gas constants in calculations
NEXT STEPS
  • Review the Clausius-Clapeyron relation and its applications in thermodynamics
  • Learn about the differences between latent heat of vaporization and change in enthalpy
  • Explore practical examples of geyser thermodynamics
  • Investigate the impact of pressure changes on boiling points using real gas equations
USEFUL FOR

Students participating in physics competitions, educators teaching thermodynamics, and anyone interested in the scientific principles governing geysers and phase changes in water.

Elemere
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Hi first post so forgive any break in widely accepted conduct,
Currently involved in a physics competition one of the question is to investigate geysers. Time and time again I have stumbled upon reference to Clausius-Clapeyron relation. Probably the best source I have come across is a youtube video and while able to replicate his results of total pressure by using his variables I am still unable to determine the heat of the water at the bottom of the geyser. Below I will paste the youtube video and my math that isn't working.

Thankyou in advance

Arrangement of relation given:
http://file:///C:/Users/ryan/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png

Values given:
P1 = aprox 100000 (atmospheric pressure)
P2 = 113000
Delta Hvap = 2.6*10^6 (latent heat of vaporization H2O)
R = 8.314 (gas constant)
T2 = ?
T1 = 100C (boiling point I assume)

When these values are input into the relation the result is 100.0045 when the video states it should be 103 inputting other values doesn't seem to move T2 far from 100.Youtube vid:
 
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I am so sorry and if someone would tell me how I could take this down I would appreciate it. I assumed Hvap was latent heat of vaporization when really it is change in enthalpy which has a value of 41000 J/mol.
 

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