# Deflating tire, thermodynamics problem

• Melgibson
In summary, the conversation discusses finding the size of a hole in a tire after it has been flat for 60 minutes. The equations used include impulse, pressure, and the derivative of the ideal gas law. The attempt at a solution involves a general equation for pressure as a function of time and determining the initial pressure. A mistake in the derivation is identified and corrected. The conversation ends with a request for clarification.
Melgibson

## 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

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:
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.

## 1. How does tire deflation affect thermodynamics?

Tire deflation can affect thermodynamics by changing the pressure and volume of the gas inside the tire. This can alter the temperature and overall energy of the gas, affecting the overall thermodynamic properties of the system.

## 2. What factors can cause a tire to deflate?

Tires can deflate due to a variety of factors, such as punctures, leaks, or changes in temperature. Other factors may include improper tire maintenance, aging of the tire, or defects in the tire itself.

## 3. How does the ideal gas law apply to a deflating tire?

The ideal gas law, which states that the pressure, volume, and temperature of a gas are all related, can be applied to a deflating tire. As the volume of the gas decreases due to deflation, the pressure and temperature will also decrease.

## 4. Can tire deflation lead to a change in the internal energy of the gas?

Yes, tire deflation can lead to a change in the internal energy of the gas inside the tire. As the gas expands and does work on the surroundings, it loses internal energy, resulting in a decrease in temperature.

## 5. How can the thermodynamic properties of a deflating tire be measured?

The thermodynamic properties of a deflating tire, such as pressure, volume, and temperature, can be measured using various tools and techniques such as pressure gauges, thermometers, and calculations based on the ideal gas law. These measurements can help determine the overall energy and efficiency of the tire.

• Mechanics
Replies
67
Views
3K
• Thermodynamics
Replies
3
Views
1K
Replies
1
Views
1K
• Science and Math Textbooks
Replies
10
Views
1K
• Classical Physics
Replies
0
Views
679
• Science and Math Textbooks
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
776
• Thermodynamics
Replies
17
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
970