Does Boyle's Law Apply to Saturated Air?

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SUMMARY

The discussion centers on the application of Boyle's Law to saturated air when the volume is halved isothermally. The initial pressure P of the saturated air does not result in a final pressure of 2P due to the loss of water vapor as the air cannot maintain saturation at the same temperature. The final pressure is less than 2P but greater than P, as the number of moles of water vapor decreases when the volume is reduced, affecting the overall pressure calculation. This highlights the importance of considering phase changes in gases under varying conditions.

PREREQUISITES
  • Understanding of Boyle's Law and its application to gases
  • Knowledge of the relationship between pressure, volume, and temperature in gases (PV=nRT)
  • Familiarity with the concept of saturation pressure and its dependence on temperature
  • Basic principles of phase changes in thermodynamics
NEXT STEPS
  • Study the implications of phase changes on gas laws in thermodynamics
  • Learn about the saturation curve and its significance in thermodynamic processes
  • Explore the concept of partial pressures and their role in gas mixtures
  • Investigate the behavior of real gases versus ideal gases under varying conditions
USEFUL FOR

This discussion is beneficial for students and professionals in physics and engineering, particularly those studying thermodynamics, fluid mechanics, and atmospheric sciences.

Amith2006
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Sir,
I have a have a doubt in the following problem:
# A volume V of air saturated with water vapour exerts a pressure P. If the volume is made V/2 isothermally, what will be the final pressure?
I solved it using Boyle's law but that answer which is "2P" doesn't agree with the answer given in my book which is "less than 2P but greater than P". Could you please explain why?
 
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Amith2006 said:
Sir,
I have a have a doubt in the following problem:
# A volume V of air saturated with water vapour exerts a pressure P. If the volume is made V/2 isothermally, what will be the final pressure?
I solved it using Boyle's law but that answer which is "2P" doesn't agree with the answer given in my book which is "less than 2P but greater than P". Could you please explain why?
For a particular temperature, the air is saturated with water vapour at a unique pressure (or you could say, the pressure determines the saturation temperature-the boiling point).

So, as you start at saturation pressure (ie at boiling point) and then increase the pressure (decrease the volume) keeping the temperature the same, the air loses saturation (the air cannot hold as much water). This means that the number of moles of water molecules in the air decreases (turns to liquid). Since PV=nRT, PV is not constant because n decreases. So P_f = n_fRT/Vf < n_iRT/Vf = 2niRT/Vi = 2Pi = 2P

AM
 

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