Fluid Mechanics: Pressure Question

[MechEngJordan]

Homework Statement

A tyre pressure gauge indicates 20 N/cm² for a tire at 34°C after a fast motorway run. Assuming that the volume of the air in the tyre is constant, atmospheric pressure is 760 mmHg and the air gas constant is 0.287 kJ/kg.K:

i) Estimate the indicated pressure when the tyre has cooled to 10°C.

ii) If the tyre is treated as a tube of cross-sectional area 0.015 m² rolled into a ring of mean diameter 0.035 m, estimate the mass of air in the tyre.

Homework Equations

Combined Gas Law:

$$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$$

Equation of State for Ideal Gas:$$pV = mRT$$

The Attempt at a Solution

For i)

Converting units into SI and recognising volume = constant gives:

$$\frac{p_1}{T_1}=\frac{p_2}{T_2}$$

$$\frac{p_1T_2}{T_1}=p_2$$

$$\frac{(200kPa)(283.15K)}{307.15K}=p_2$$

$$p_2 = 184kPa$$

I am unsure how exactly how to proceed with ii)

Any help would be appreciated.

 

[SteamKing]

Do you know how to calculate the volume inside the tire given the data in part ii?

If you know the volume, the temperature, and the pressure, can you calculate the mass of air consistent with these properties?

 

[MechEngJordan]

Do you know how to calculate the volume inside the tire given the data in part ii?

If you know the volume, the temperature, and the pressure, can you calculate the mass of air consistent with these properties?

I am unsure of how I would calculate the volume -- which is particularly annoying, as I am aware that would solve my problem by application of the ideal gas law.

 

[tms]

The shape of the tube is called a torus. Think of it as a cylinder with the ends connected. Calculate the volume in the obvious, straightforward fashion.

 

[MechEngJordan]

Thanks for the help.