A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 40.0 psi. If the pump is a cylinder of length 18.0 in. with a cross-sectional area of 3.00 in2 . , how far down must the piston be pushed before air will flow into the tire?
1 Answer
In order that air flows into the tire, the pressure in the pump must be more than the tire pressure,
We assume that air follows ideal gas equation, the temperature of the compressed air remains constant as the piston moves down. Taking one atmospheric pressure to be
# PV=nRT# .
As number of moles of air do not change during its compression in the pump, RHS of the gas equation is constant. Therefore we have
#P_1V_1=P_2V_2#
where#1 and 2# are initial and final states respectively.
Inserting various values we get
#14.7xx(18.0xx3.00)=(14.7+40)V_2#
#=>V_2=(14.7xx(18.0xx3.00))/(14.7+40)#
#=>V_2=14.512\ "in"^3#
Length of pump, measured from bottom, this volume corresponds to is
#14.512/3.00=4.8\ "in"#
Piston must be pushed down by more than
#18.0-4.8=13.2\ "in"#