A bicycle pump contains 20 cm3 of air at a pressure of 100 kPa. The air is then pumped in a tyre of volume 100 cm3. Calculate th

Question

2 years ago

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e pressure of the air in the tyre. Assume that the temperature is fixed.

1 answer:

Natasha2012 [34] · Answer 1 · 2022-08-12T14:22:16+03:00

Answer:

The pressure of the air in the tyre is 20 kPa

Explanation:

The parameters for the bicycle pump and tyre are;

The volume of air contained in the bicycle pump, V₁ = 20 cm³

The pressure of the air contained in the bicycle pump, P₁ = 100 kPa

The volume (available) of the tyre, where the air is pumped, V₂ = 100 cm³

Let P₂ represent the pressure in the tyre after the air is pumped

By Boyle's law, we have that at constant temperature, the volume of a given mass of gas is inversely proportional to its pressure;

Mathematically, Boyle's law gives the following equation;

P₁ × V₁ = P₂ × V₂

∴ P₂ = (P₁ × V₁)/V₂

Substituting the known values gives;

P₂ = (100 kPa × 20 cm³)/(100 cm³)

∴ P₂ = 100 kPa × 1/5 = 20 kPa

P₂ = 20 kPa

The pressure of the air in the tyre = P₂ = 20 kPa.