Which room contains the greater mass of air?

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SUMMARY

In the discussion regarding the mass of air in two connected rooms, it is established that both Room A and Room B have the same volume and pressure, but differ in temperature. Room A, being warmer, contains a greater number of moles of air due to the ideal gas law (PV=nRT), where the number of moles (n) increases with temperature (T) when pressure (P) and volume (V) are constant. Therefore, Room A has a greater mass of air compared to Room B.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of the relationship between temperature and the number of moles of gas
  • Familiarity with basic thermodynamics concepts
  • Ability to perform calculations involving pressure, volume, and temperature
NEXT STEPS
  • Study the implications of the Ideal Gas Law in real-world scenarios
  • Explore the concept of molar mass and its calculation
  • Learn about the effects of temperature on gas behavior
  • Investigate the principles of thermodynamics related to gas mixtures
USEFUL FOR

Students studying physics or chemistry, educators teaching gas laws, and anyone interested in thermodynamics and the behavior of gases under varying conditions.

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Homework Statement



Rooms A and B are the same size and are connected by an open door. Room A however, is warmer(perhaps because its windows face the sun). Which room containks the grater mass of air? explain carefully.


Homework Equations



PV=nRT, PV=NkT, N=Na*n


The Attempt at a Solution



Va=Vb=V. The problem didn't mention it but I am also going to assume both rooms have the same pressure, which is the atmospheric pressure. I think the key factor that will determine which room will have the larger mass is the number of moles, since you can multiply the number of moles by the molar mass to get the mass of a molecule or compound. Am I correct?
 
Physics news on Phys.org
Yes, that's correct.

P and V are the same for the two rooms. It's n and T that are different.
 

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