Average Force of Oxygen Molecule in Cubical Vessel

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SUMMARY

The average force exerted by an oxygen molecule on the walls of a cubical vessel measuring 0.10 m per side can be calculated using the formula F = dp/dt. Given the mass of the oxygen molecule as 5.32E-26 kg and its root mean square velocity (νrms) of 484 m/s, the force can be derived from the change in momentum over time. The relevant equation for this calculation is dPx/dt = (N * A * M * vx2) / V, where N is the number of molecules, A is the area of the wall, M is the mass of the molecule, and V is the volume of the vessel.

PREREQUISITES
  • Understanding of momentum and force equations in physics
  • Familiarity with the concept of root mean square velocity
  • Knowledge of basic thermodynamics principles
  • Ability to perform calculations involving mass, area, and volume
NEXT STEPS
  • Study the derivation of the momentum change formula F = dp/dt
  • Learn about the kinetic theory of gases and its applications
  • Explore the implications of molecular motion in confined spaces
  • Investigate the relationship between temperature and molecular speed
USEFUL FOR

Students in physics, particularly those studying thermodynamics and kinetic theory, as well as educators and researchers interested in molecular dynamics and gas behavior.

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Homework Statement


...Suppose an oxygen molecule (m=5.32E-26 kg) traveling at this speed ([itex]\nu_{rms}=484 m/s[/itex]) bounces back and forth between opposite sides of a cubical vessel 0.10 m on a side. What is the average force the molecule exerts on one of the walls of the container? (Assume that the molecule's velocity is perpendicular to the two sides that it strikes.)

Homework Equations


[itex]F=\frac{dp}{dt}[/itex]

The Attempt at a Solution


I can't remember how to do this, even after looking through my notes.
 
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Nevermind, I found it.

[tex]\frac{dP_x}{dt}=\frac{NAMv_x^2}{V}[/tex]
 

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