Question

A gas cylinder has a volume of 0.4 m”. It contains
butane at a pressure of 100 kPa and a temperature of
20°C. What pressure is needed to compress the gas
to a volume of 0.05 m at the same temperature?​

Answer 1

Given :

• Initial volume of gas ( V₁ ) = 0.4m³
• Initial pressure of gas ( P₁ ) = 100kPa
• Initial temperature of gas ( T₁ ) = 20°C
• Final volume of gas ( V₂ ) = 0.05 m³
• Final Temperature of gas ( T₂ ) = 20°C

To find :

Final pressure of gas ( P₂ )

Solution :

As given that temperature of gas remain constant during compression, we can apply Boyle's law.

According to Boyle's law , pressure of gas is inversely proportional to the volume of gas when temperature remain constant. that is , P ∝ (1/V)

➝ (P₁)/(P₂) = (V₂)/(V₁)

➩ 100 kPa/ (P₂) = 0.05 m³/0.4m³

➩ (P₂) = 100 kPa × 0.4 /0.05

➩ (P₂) = 40/0.05 kPa

➩ (P₂) = 4000/5 kPa

➩ (P₂) = 800 kPa

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ANSWER : 800 kPa