Answer to Question #283151 in Physics for Kimgcash

Question

. A bicycle tyre has a volume of 1.2 x 10-3 m3 when fully inflated. The barrel of the pump

has a working volume of 9 x 10-5 m3. Assume that the inflation takes place slowly and

no heating occurs.

How many strokes of the pump are required to inflate the tyre from being completely

flat (no air inside) to its fully inflated pressure (3.0 x 105 Pa) and volume?

Why will the bicycle pump get hot if you’re pumping quickly?

Answer 1

Assuming constant temperature, the volume of the tire of 1.2x10^-3 m³ at normal pressure takes another value at 3.0x10⁵ Pa:

$$P_0V_0=P_1V_1,\\\space\\ V_0=P_1V_1/P_0=3.55·10^{-3}\text{ m}^3,\\\space\\ N=\dfrac{V_0}{v}=\dfrac{3.55·10^{-3}}{9·10^{-5}}=40.$$

The bicycle pump gets hot if you’re pumping quickly because the air quickly compresses and you increase the energy of the molecules.