A bicycle pump contains 250cm3 of air at a pressure of 90kPa. If the air is compressed , the volume is reduced to 200cm3. What is the pressure of the air inside the pump?
P V = n R T
if n , R and T are constant then
P1 V1 = P2 V2
P2 = P1 (V1/V2)
Assuming that T is constant is needed but unreliable because in real life the pump will heat up.
To find the pressure of the air inside the pump after it is compressed, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume, given a constant temperature.
Boyle's Law can be expressed as:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure of the air inside the pump (90 kPa)
V1 = Initial volume of the air inside the pump (250 cm^3)
P2 = Final pressure of the air inside the pump (unknown)
V2 = Final volume of the air inside the pump (200 cm^3)
Rearranging the formula, we get:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (90 kPa * 250 cm^3) / 200 cm^3
P2 = (22500 kPa*cm^3) / 200 cm^3
P2 = 112.5 kPa
Therefore, the pressure of the air inside the pump after it is compressed is approximately 112.5 kPa.