Temperature of Air escaping from tire

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Discussion Overview

The discussion revolves around calculating the temperature of air escaping from a tire after it has been inflated. Participants explore the concept of adiabatic cooling and the relevant equations, considering both theoretical and practical implications of the process.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant mentions the use of the ideal gas law (PV = nRT) in relation to adiabatic cooling.
  • Another participant introduces an equation for adiabatic expansion, relating initial and final temperatures and volumes, and defines the ratio of specific heats, γ.
  • A participant questions the definition of the final volume (Vf) of the escaping air, suggesting it may relate to the rate of air escaping rather than a fixed volume.
  • Concerns are raised about the role of air velocity and nozzle size in the expansion process.
  • A participant references the possibility of temperature changes during expansion, mentioning phenomena like inversion lines that could lead to both temperature decreases and increases.
  • A later reply suggests that calculating the volume of air outside the tire at atmospheric pressure can be straightforward.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of certain equations and concepts, particularly regarding the final state of the air and the factors influencing temperature changes during expansion. No consensus is reached on these points.

Contextual Notes

Participants highlight potential limitations in defining the final state of the air and the assumptions involved in applying the equations discussed. The discussion does not resolve these uncertainties.

Who May Find This Useful

Individuals interested in thermodynamics, fluid dynamics, or practical applications related to tire pressure and air expansion may find this discussion relevant.

agurule
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I have been trying to understand how to calculate the temperature of the air escaping from a blown up tire. I know its adiabatic cooling - but is it as simple as PV = nRT?
Thanks
 
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An adiabatic expansion goes as:

[tex]T_i V_i^{\gamma-1} = T_f V_f^{\gamma-1}[/tex]

where [itex]\gamma \equiv C_p/C_v[/itex].

- Warren
 
In your equation
1. the i state (T, V) is the state of the air initally, in the tire. I have a tire that has a certain volume (Vi) and is at some temperature (Ti)
2. the f state is the final state, air coming out of the tire - I understand Tf - what is Vf since the air is escaping to the great outdoors. Is it the amount of air that is escaping - per unit time?

Why doesn't velocity of air come into equation
size of nozzle

Under expansion, such as though a JT valve, can't I expand air such that in some cases it gives me a decrease in temperature, and in some cases an increase in temperature - something called an inversion line.

THANKS
 
You can easily calculate how much volume the air will occupy once outside the tire (and thus at 1 atm pressure).

- Warren
 

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