Question

Chapter: The Gas Laws

The air in a bicycle tyre has a volume of 1000 cm^3 and a pressure of 2.5 atmospheres. If the air is released (at the same temperature) so its pressure is 1.0 atmosphere, what is the volume of the air?

A bicycle pump has a volume of 100 cm^3 and is now used to pump up the tyre. After 1 stroke of the pump, what is the pressure in the tyre?

Answer 1

1. The volume of the air is 2500 cm³

2. The pressure in the tyre is 2.27 atm

Boyle's law equation

P₁V₁ = P₂V₂

Where

• P₁ is the initial pressure
• V₁ is the initial volume
• V₂ is the new volume
• P₂ is the new pressure

1. How to determine the new volume

• Initial pressure (P₁) = 2.5 atm
• Initial volume (V₁) = 1000 cm³
• New pressure (P₂) = 1 atm
• New volume (V₂) = ?

P₁V₁ = P₂V₂

2.5 × 1000 = 1 × V₂

V₂ = 2500 cm³

Thus, the volume of the air is 2500 cm³

2. How to determine the new pressure

• Initial pressure (P₁) = 2.5 atm
• Initial volume (V₁) = 1000 cm³
• New volume (V₂) = 1000 + 100 = 1100 cm³
• New pressure (P₂) = ?

P₁V₁ = P₂V₂

2.5 × 1000 = P₂ × 1100

Divide both sides by 1100

P₂ = (2.5 × 1000) / 1100

P₂ = 2.27 atm

Thus, the pressure in the tyre is 2.27 atm

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