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

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Solution

Volume of gas $(V_{1}) = 500 d m^{3}$
Pressure of gas $(P_{1}) = 1$ bar
Compressed gas volume $= V_{2} = 200 d m^{3}$
$P_{2}$ be the compressed gas pressure
Boyels law [constant temperature]
$P_{1} V_{1} = P_{2} V_{2}$
$P_{2} = \frac{P_{1} V_{1}}{V_{2}}$
$= \frac{1 \times 500}{200}$
$P_{2} = 2.5$ bar.
Minimum pressure required is $2.5$ bar.

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