How many air molecules are there inside the tire?

That's where the extra 101,000 comes from. In summary, to calculate the number of air molecules inside a car tire with a volume of 10 L and a gauge pressure of 30 psi at 20°C, the ideal gas law (N = PV/kbT) is used. However, since the question provides gauge pressure, which is relative to ambient pressure, it needs to be converted to absolute pressure by adding atmospheric pressure (101,000 Pa or 14.7 psi). This results in a different number of air molecules: 7.6 x 10^23, compared to the initial calculation of 5.12 x 10^23.
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SmugBug
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Homework Statement



A car tire has a volume of 10 L and is inflated to a gauge pressure of 30 psi (207,000 Pa) at 20°C. How many air molecules are there inside the tire?

Homework Equations


N = PV/ kbT

The Attempt at a Solution



(207,000 Pa )x (0.01 m3) / (1.38 x 10^-21 x 293) =5.12 x 10^23

However, my instructor's answer is:
( 101,000 + 207,000 Pa )x(0.01 m3) / (1.38 x 10-21 x 293) = 7.6 x 10^23

Where is he getting that extra 101,000 that he is adding to the pressure??
 
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  • #2
SmugBug said:
Where is he getting that extra 101,000 that he is adding to the pressure??
Gauge pressure means the pressure that would be shown on a standard pressure gauge. That would be relative to ambient pressure. For the calculation you need absolute pressure, so atmospheric pressure must be added.
 
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  • #3
30 psi is the gauge pressure. A gauge under atmospheric pressure reads zero.

Edit: oops haruspex said it first
 
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A gauge pressure of 30 psi means an absolute pressure of 30+14.7= 44-7 psi. The ideal gas law uses the absolute pressure, not the gauge pressure.
 

FAQ: How many air molecules are there inside the tire?

1. How is the number of air molecules inside the tire calculated?

The number of air molecules inside the tire can be calculated using the ideal gas law, which states that the number of molecules (n) is equal to the pressure (P) multiplied by the volume (V) divided by the gas constant (R) multiplied by the absolute temperature (T). This can be expressed as n = (PV)/(RT).

2. Does the size of the tire affect the number of air molecules inside?

Yes, the size of the tire does affect the number of air molecules inside. The volume of the tire is a key factor in calculating the number of molecules, as seen in the ideal gas law equation. A larger tire will have a greater volume and therefore a higher number of air molecules compared to a smaller tire.

3. How does the type of gas used in the tire affect the number of air molecules?

The type of gas used in the tire does not significantly affect the number of air molecules. The ideal gas law is based on the assumption that all gases behave in the same way, regardless of their composition. Therefore, the type of gas used in the tire does not impact the number of molecules, as long as the conditions (pressure, volume, temperature) remain constant.

4. Can the number of air molecules inside the tire change over time?

Yes, the number of air molecules inside the tire can change over time. This is due to factors such as temperature changes, air leaks, and tire wear. As the tire heats up, the air molecules inside will gain energy and increase in volume, leading to a higher number of molecules. Air leaks and tire wear can also cause a decrease in the number of molecules by allowing some of the air to escape.

5. Is it possible to accurately count the number of air molecules inside the tire?

No, it is not possible to accurately count the number of air molecules inside the tire. The ideal gas law provides a way to calculate an estimated number, but it is difficult to measure the exact pressure, volume, and temperature inside the tire. In addition, the number of molecules is constantly changing due to external factors, making it impossible to get an exact count.

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