Properties of Matter || Solved Numericals

Q1: The pressure on 9cm³ of oxygen gas is doubled at a fixed temperature. What will its volume become?

Given:
Initial Volume, V₁ = 9 cm³
Initial Pressure, P₁ = P
Final Pressure, P₂ = 2P (doubled)
Temperature = constant

Formula: Boyle's Law: P₁V₁ = P₂V₂

Calculation:
P × 9 = 2P × V₂
9P = 2P × V₂
V₂ = 9P / 2P
V₂ = 4.5 cm³

Answer: 4.5 cm³

Q2: A container holds 30m³ of air at a pressure of 150000Pa. If the volume changed to 10m³ by decreasing load on the piston. What will the pressure of the gas become? Assume that its temperature remains constant.

Given:
Initial Volume, V₁ = 30 m³
Initial Pressure, P₁ = 150000 Pa
Final Volume, V₂ = 10 m³
Temperature = constant

Formula: Boyle's Law: P₁V₁ = P₂V₂

Calculation:
150000 × 30 = P₂ × 10
4500000 = P₂ × 10
P₂ = 4500000 / 10
P₂ = 450000 Pa

Answer: 450000 Pa or 4.5 × 10⁵ Pa

Q3: Air at atmospheric pressure of 760 mm of Hg is trapped inside a container available with a moveable piston. When the piston is pulled out slowly so that the volume is increased from 100dm³ to 150dm³, the temperature remaining constant. What will be the pressure of the air becomes?

Given:
Initial Pressure, P₁ = 760 mm of Hg
Initial Volume, V₁ = 100 dm³
Final Volume, V₂ = 150 dm³
Temperature = constant

Formula: Boyle's Law: P₁V₁ = P₂V₂

Calculation:
760 × 100 = P₂ × 150
76000 = P₂ × 150
P₂ = 76000 / 150
P₂ = 506.67 mm of Hg

Answer: 506.67 mm of Hg