What will be the minimum pressure required to compress 500 $d m^{3}$ of air at 1 bar to 200 $d m^{3}$ at $30^{0} C$ ?

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Solution

Volume of gas(V₁) = 500dm³ (given)

Pressure of gas (p₁) = 1 bar (given)

Volume of compressed gas (V₂) = 200dm³ (given)

Now, let P₂ be the pressure required to compress the gas.
Boyle’s Law states that the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.

Therefore at constant temperature P₁ V₁ = P₂ V₂ (Boyle’s Law)

As a result P₂ = $fraction numerator P subscript 1 V subscript 1 over denominator V subscript 2 end fraction$ = $fraction numerator 1 cross times 500 over denominator 200 end fraction$ = 2.5 bar

Therefore, the minimum pressure required is 2.5 bar.

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