Relative Humidity Changes in a Closed Room

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SUMMARY

The discussion focuses on calculating the mass of water vapor that must be removed from a closed room with a volume of 2000 cubic meters to reduce the relative humidity from 80% to 50% at a constant temperature of 25 degrees Celsius. The density of water vapor in saturated air at this temperature is 22.8 g/m³. The correct calculation reveals that 13.8 kg of water vapor must be removed, correcting the initial miscalculation of 6.9 kg. The discrepancy arises from misunderstanding the relationship between relative humidity and water vapor pressure.

PREREQUISITES
  • Understanding of relative humidity and its calculation
  • Knowledge of water vapor density at different temperatures
  • Familiarity with basic thermodynamic principles
  • Ability to perform unit conversions and algebraic manipulations
NEXT STEPS
  • Review the concept of water vapor pressure and its relation to relative humidity
  • Study the properties of air and water vapor at various temperatures
  • Learn about the ideal gas law and its applications in humidity calculations
  • Explore practical applications of humidity control in HVAC systems
USEFUL FOR

Students studying thermodynamics, HVAC engineers, and anyone interested in environmental control systems will benefit from this discussion.

slaw155
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Homework Statement


A room with volume 2000 cubic metres has air at T=25degrees Celsius with relative humidity 80%. Density of water vapor in saturated air at 25deg Celsius is 22.8g/m^3. Temperature and pressure of room remains constant. What mass of water vapor must be removed from this air to reduce relative humidity to 50%?

Homework Equations



relative humidity/100 = water vapor pressure/saturated water pressure

The Attempt at a Solution


using above formula and density definition we get (18.3x2000)-(11.4x2000) = 6.9kg.
However the textbook answer is double this? Where have I gone wrong?
 
Last edited:
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slaw155 said:
using density = mass/volume we get (18.3x2000)-(11.4x2000) = 6.9kg.
Try that computation again.
 

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