Question

What will be the minimum pressure required to compress 500 [tex]dm^{3} [\tex] of air at 1 bar to 200 [tex]dm^{3} [\tex] at 30°C ?
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Answer 1

Given:

✰ Volume of gas ( V₁ ) = 500 dm³

✰ Pressure of gas ( P₁ ) = 1 bar

✰ Volume of compressed gas ( V₂ ) = 200 dm³

✰ Temperature is constant at 30°C

To find:

✠ The minimum pressure required to compress the gas.

Solution:

We will solve this question by using Boyle's law, which states that the volume of a given mass of a diagram is inversely proportional to its pressure at constant temperature. P₁V₁ = P₂V₂ ( at constant temperature ) We will use this expression and by substituting the values of P₁V₁ and V₂ and doing required calculations, we can easily get the value of P₂ which is equal to the minimum pressure required to compress the gas.

Let P₂ be the minimum pressure required to compress the gas.

By using Boyle's law,

✭ P₁V₁ = P₂V₂ ✭

Substituting the values,

➤ 1 × 500 = P₂ × 200

➤ P₂ = (1 × 500)/200

➤ P₂ = 500/200

➤ P₂ = 5/2

➤ P₂ = 2.5 bar

∴ The minimum pressure required to compress the gas = 2.5 bar

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Answer 2

$\huge{\underline{\mathcal\purple{Question:}}}$

$\mathcal{What \: will\: be\: the\: minimum \: pressure \: required\: }$

$\mathcal{ to \: compress\: 500 dm^{3}\: of \: air \: at \: 1\: bar\: to\: 200\: dm^{3} \: at\: 30°C?}$$\huge{\underline{\mathcal\green{Given:}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\mathcal{Intial \: volume \: = \: 500 {dm}^{3}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\mathcal{Final \: volume = \: 200 \: d {m}^{3}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\mathcal{Intial \: Pressure = 1 \: bar}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\mathcal{Final\: Pressure(P2)\: ?}$

$\large\mathcal\red{\underline{\overline{\mid{\blue{Answer}}\mid}}}$

$\mathcal{We \: know \: that \: temperature \: remains \: constant \: at \: 30°C.}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathcal{\underline{ According \: to \: boyle's \: law,}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathcal{P1 \times V1=P2 \times V2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathcal{P2= \dfrac{P1 \times V1}{v2}}$

$\: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \mathcal{ \:P2= \dfrac{1 \times 500}{ 200} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \mathcal{P2 \: = \dfrac{500}{200}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathcal{P2 \: = \dfrac{5}{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \mathcal{P2 = 2.5 \: bar}$