Question

A piston in a bicycle pump is pressured half way into the pump without letting air get out and at unchanged temperature. Inside diameter of the pump is 2,3 cm.
a) What is the pressure inside the pump in atm?
b) How much force is needed to hold the piston in this position?


The answers are 2.0 atm and 42 N.
Can someone please explain how do I get these answers? :)

Answer 1

P V = NRT = constant if n and T constant
so
P1 V1 = P2 V2
if V2 is half V1
then
P2 is TWICE P1

difference in pressure from one side of piston to the other = 1 atm which is about 10^5 Pascals or Newtons.m^2

F = P A = 10^5 newtons.m^2 * pi .23^2 / 4