The end result, the weight of the tire, is a force. What is force? Mass times acceleration. Acceleration is the acceleration due to gravity. Therefore, the mass is required to complete the solution. The mass is found using a form of the ideal gas equation:
PV = mRT
rearranging,
m =
PV
RT
Pressure The pressure given in the statement is the gage pressure – the absolute pressure is the value needed for the ideal gas equation.
The standard atmospheric pressure = 14.7 lbf / in2, so the absolute pressure is:
Pabs = 33 lbf/in2 + 14.7 lbf/in2 = 47.7 lbf/in2
Gas Constant There are values for R in terms of lbm (click here) but lbm must be converted into units of lbf. For more info about this click here. The slug is a unit of mass that takes into account lbf.
The value of R for air is then:
R = 1716
ft*lbf
slug*R
Temperature For temperature it is simple unit conversion. Convert °C to °F then to R.
Mass Calculation It is important when calculations start to involve a big jumble of units to write them all down to make sure they cancel out. Using the modified form of the ideal gas law equation from above:
m =
(
47.7 lbf
in2
)
*
(
2.5 ft3
1
)
*
(
12 in
ft
)
*
(
12 in
ft
)
(
1716 ft*lbf
slug*R
)
*
(
slug*ft
lbf*s2
)
*
(
531.29 R
1
)
= 0.01884
lbf
ft / s2
You can PrntScrn, paste into MSPaint, and see that all the units cancel out besides
lbf
ft / s2
which is mass.
Final Answer Now that mass and gravitational acceleration are known, the weight of the air can easily be found: