Help needed for this question - Air pressure in a bike tire

In summary, the pressure in a bike tire is 9 bar at sea level on a day when the temperature is 21°C. The pressure in the tire is the gauge pressure and the actual pressure is 7 bar.
  • #1
andyb1990
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0
Help needed for this question -- Air pressure in a bike tire

Homework Statement


The Pressure gauge on a bike pump reads 8 bar at sea level on a day when the temperature is 21°C. Assume that the gas constant for air is 286.9 J/Kg K

a) What is the density of the air in the tyre?

b) What is the weight of the air in the tyre, if the diameter of the wheel is 0.66m and the diameter of the inner tube is 4cm
Help would be greatly appreciated

also in SI units please :)

Homework Equations


The Attempt at a Solution


pv=mRT

p= 8bar
R= 286.9
T= 273+21 294

m=?

equation V=mRT/P?
 
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  • #2


Some notes:
The pressure in the tire is the gauge pressure ... what is the actual pressure?
You can construct the state equation for the gas in the tire OK?
Density is mass-per-unit-volume, though you can have a molar density as the number of moles per unit volume ... that would be (m/V) right?
... that should take care of part (a) ... having got the density, you should be able to get the mass from the volume for part (b).
 
  • #3


so the pressure will be...

(Pgage = ρgh??) + (pressure of atmosphere 101325pa * temp 21°)
 
  • #4


andyb1990 said:
so the pressure will be...

(Pgage = ρgh??) + (pressure of atmosphere 101325pa * temp 21°)

1. p ~ 8 + 1 = 9 bar. What's with "ρgh"??

I suppose you can be more precise & include T effect.

2. You said pV = mRT, so rewrite this substituting density ρ. I would not mess with moles, no need and no point.

3. Rest is straightforward.
 
  • #5


The rude man is correct - a tire gauge compares the pressure of the atmosphere outside the tire with the pressure of the air inside it... reading out the difference. So:[tex]P_{gauge}=P_{actual}-P_{atmos}[/tex]

Keep going... :)
 
  • #6


so the equation including density would look likeP=ρ(R/M)Tsorry I just can't get my head around it! :(

and the actual pressure would be 7bar?
 

1. How do I know the correct air pressure for my bike tire?

The correct air pressure for a bike tire depends on the type of bike and tire, as well as the weight of the rider. Generally, road bikes require between 80-130 psi, while mountain bikes may need 25-35 psi. It's best to consult the manufacturer's recommendation or ask a bike expert.

2. Why is it important to maintain proper air pressure in bike tires?

Proper air pressure in bike tires is crucial for optimal performance and safety. Inflating tires to the recommended pressure ensures better handling, reduces the risk of flats, and extends the life of the tire.

3. How often should I check the air pressure in my bike tires?

It's recommended to check the air pressure in your bike tires before every ride. Tires can lose pressure over time, and slight changes in temperature can also affect the pressure. Regularly checking and adjusting the air pressure will ensure a smooth and safe ride.

4. Can I use a regular tire pump to inflate my bike tires?

Yes, you can use a regular tire pump to inflate your bike tires. However, it may take longer to reach the recommended pressure, and you may need a separate adapter to fit the valve of your bike tire.

5. Is it safe to overinflate bike tires?

No, it is not safe to overinflate bike tires. The recommended air pressure is determined for optimal performance and safety. Overinflating tires can cause them to burst, which can be dangerous for the rider. Always follow the manufacturer's recommendation for the correct air pressure.

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