Hi all,
Is there any book you recommend for thermo?
Here is the question for thermodynamics:
The volume of my bicycle tyre is 1.5L. It is meant to be pumped to 40 psi guage ("guage" means above atmosphere pressure, ie. 55 psi absolute). The dimensions of the bicycle pump are 20mm diameter with a stroke of 300mm. How many times will I have to pump if the pump is 80% efficient on average?
I hope someone can help! lol
Thank you
If by efficiency it means that 80% of the mass of gass in the cylinder is
transfered into the tyre on one stroke we can do something.
The perfect gass law tells us that at constant temprature:
pV=Km,
where p is the pressure, V the volume, m the mass, and K a constant
which in this case will be related to the gas constant per unit mass,
temprature and the units that everything else is measured in.
(and while the temprature of the air in the pump will change during a stroke
the initial temprature in the pump will be ambient, and the final temprature
in the tyre will also be ambient. So the required calculations can all be done
using assuming constant initial and final temprature)
Then the mass transfered on a single stroke of the pump is:
m_p=0.8 x 10 x (60)/K.
The initial mass in the tyre is:
m_0=10 x (1500)/K
and the final mass:
m_1=55 x (1500)/K
(1500 is 1.5 litres in cc's, and 60 is the volume of the pump
cylinder in cc's)
So the change in the mass of air in the tyre is:
deltam=45 x (1500)/K
which is the mass transfered by:
N= [45 x (1500)/K] / [0.8 x 10 x (60)/K] =140.625
strokes of the pump.
(Note we can use dreadfully mixed units here as all the conversion
factors are absorbed into K, which convieniently cancells out)
RonL