Changes in Density of Water Vapor Under Constant Volume and Temperature

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SUMMARY

The discussion focuses on calculating the density change of water vapor when heated from 403.15 K to 463.15 K at a constant volume of 3 m² and an initial pressure of 10^5 Pa. The relevant equations include the ideal gas law (PV = nRT) and the density formula (D = M/V). Participants explored the relationship between pressure and temperature using the formula P_2 = P_1 * (T_2/T_1) to find the final pressure, but faced challenges due to the unknown mass (M) of the vapor.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = nRT)
  • Knowledge of density calculation (D = M/V)
  • Familiarity with temperature scales (Kelvin)
  • Basic principles of thermodynamics
NEXT STEPS
  • Study the derivation and application of the Ideal Gas Law in real-world scenarios
  • Learn about the relationship between pressure, volume, and temperature in thermodynamic processes
  • Explore methods to calculate mass from pressure and density
  • Investigate the effects of heating on gas density and pressure changes
USEFUL FOR

Students in physics or engineering, particularly those studying thermodynamics, as well as professionals involved in HVAC systems, meteorology, or any field requiring knowledge of gas behavior under varying temperatures and pressures.

renlok
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Homework Statement


water vapor is heated from 403.15k to 463.15k and is kept at a constant volume of 3m^2 its initial pressure is 10^5pa what is the density change?


Homework Equations


PV = nRT, D = M/V


The Attempt at a Solution


I don't really know where to go with this i found the final pressure with [tex]P_2 = \frac{P_1.T_2}{T_1}[/tex] but I am not sure this helped i also tried with P(M/D) = nRT but as you don't know M its not very helpful. I also though about using [tex]\delta{M} = \frac{\delta{E}}{c^2}[/tex] but couldn't find E without the mass...
 
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renlok said:

Homework Statement


water vapor is heated from 403.15k to 463.15k and is kept at a constant volume of 3m^2 its initial pressure is 10^5pa what is the density change?


Homework Equations


PV = nRT, D = M/V


The Attempt at a Solution


I don't really know where to go with this i found the final pressure with [tex]P_2 = \frac{P_1.T_2}{T_1}[/tex] but I am not sure this helped i also tried with P(M/D) = nRT but as you don't know M its not very helpful. I also though about using [tex]\delta{M} = \frac{\delta{E}}{c^2}[/tex] but couldn't find E without the mass...
You have that the density ρ is the mass of the steam M divided by the volume V it occupies. How did M and V change when the water vapor was heated?
 

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