How Do You Calculate Final Pressure in Connected Gas Containers?

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SUMMARY

The discussion centers on calculating the final pressure in connected gas containers using the ideal gas law. The initial pressures are P1 = 3 x 10^5 Pa and P2 = 2 x 10^5 Pa, with temperatures T1 = 600 K and T2 = 200 K. The user attempts to find the final pressure (Pf) using the equation P1V1/T1 = PfVf/Tf but initially arrives at an incorrect value. The correct approach involves considering the total volume and the conservation of gas, leading to the final pressure being determined through the proper application of the ideal gas law.

PREREQUISITES
  • Understanding of the ideal gas law and its applications.
  • Knowledge of pressure, volume, and temperature relationships in gas laws.
  • Familiarity with unit conversions, particularly in the context of pressure (Pa).
  • Basic algebra skills for manipulating equations.
NEXT STEPS
  • Study the ideal gas law and its derivation for connected systems.
  • Learn about the concept of gas conservation in closed systems.
  • Explore the implications of temperature changes on gas pressure and volume.
  • Practice solving problems involving multiple gas containers and equilibrium states.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, physics enthusiasts, and anyone involved in gas laws and pressure calculations in connected systems.

FahimP
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Homework Statement



Two containers contain the same gas at different temperatures and pressures, as indicated in the figure. The small container has a volume of 1 L, and the large container has a volume of 2 L. The two containers are then connected to each other using a thin tube, and the pressure and temperature in both containers are allowed to equalize. If the final temperature is 219 K, what is the pressure.

Givens :
P1 = 3 x10 ^ 5
P2 = 2 x 10 ^5
T1 = 600k
T2 = 200K

Homework Equations


P1V1/T1 = P2V2/T2

The Attempt at a Solution



I used this equation to find final pressure
P1V1/T1 = PfVf / Tf
i solved for Pf and I got like 7300. I know the answer has to be between the given pressures but I don't think I am using the right equation. I also used this equation which i made up P1V1/T1 + P2V2/T2 = PfVf/Tf ---> which didnt work any advice or tips
 
Last edited:
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what units is the pressure given in?
 
What is total amount of gas after connecting the tanks? What is total volume?
 

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