Deflating tire, thermodynamics problem

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SUMMARY

The discussion focuses on calculating the size of a hole in a tire after it has deflated over 60 minutes. Key equations utilized include the impulse equation (Impulse = F*Δt = ΔN*Δp) and the ideal gas law derivative (dPV = dNkT). The user derived a pressure decrease function, P = e^(-((A√(kT)/(2V√(m))) * t) + P(initial)), but initially struggled with determining the initial pressure. The user identified a mistake in their integration process, realizing the need for an additional constant in their equation.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically the ideal gas law.
  • Familiarity with calculus, particularly integration techniques.
  • Knowledge of pressure, area, and force relationships in physics.
  • Basic grasp of kinetic theory of gases and impulse-momentum concepts.
NEXT STEPS
  • Study the ideal gas law and its applications in real-world scenarios.
  • Learn about the kinetic theory of gases and its implications for pressure and volume.
  • Explore advanced integration techniques in calculus relevant to physics problems.
  • Investigate impulse-momentum relationships in various physical systems.
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone involved in mechanical engineering or automotive repair who seeks to understand the dynamics of tire deflation.

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Homework Statement


Find the size of the hole in the tire after it has taken 60minutes to become flat.

Homework Equations


Impulse = F*Deltat = DeltaN*Deltap (N=molecules, p=momentum) , P = F/A (A is area of hole), Equipartition for gas in 1-d -> 1/2kT = 1/2mv^2
Derivative of ideal gas law (assuming T and V are constant) = dPV=dNkT

The Attempt at a Solution


the general equation i came up with that describes the decrease in pressure as a function of time is P = e^-((Aroot(kT)/(2Vroot(m)) *t) + P(initial)) actually ill upload a typed image
flkqyv.jpg


Using a known volume of a tire i am trying to find the initial pressure but I am having trouble figuring out how to do it any help would be appreciated. Also I am not sure if i have made a mistake in deriving this equation

Ummm have i explained well enough? Is there more i need to include? Or is the answer not simple? I am sort of waiting for an update if someone could clarify it would be nice.
 
Last edited:
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Oh i see where i made the mistake. After the integration there should be 1 constant on each side to be combined into another constant which is not P(initial). What a silly mistake. From there it is pretty straightforward.
 

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