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

[andyb1990]

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?

 

[Simon Bridge]

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).

 

[andyb1990]

so the pressure will be...

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

 

[rude man]

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.

 

[Simon Bridge]

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:P_{gauge}=P_{actual}-P_{atmos}

Keep going... :)

 

[andyb1990]

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?