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# What will be the minimum pressure required to compress 500 dm ^3 of air at 1 bar to 200 dm ^3 at 30 ^o C ?

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

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Given the volume of air to be compressed is $500dm^3$ at $1 bar$ pressure to $200dm^3$ at $30^{\circ}C$.

So, as the temperature remains constant at $30^{\circ}C$.

We have Boyle's law where, $P_{1}V_{1} = P_{2}V_{2}$

To calculate the final pressure $P_{2}$.

We have,

$P_{1}V_{1} = P_{2}V_{2}$

$P_{2} = \frac{P_{1}V_{1}}{V_{2}}$

$= \frac{1\times 500}{200} bar = 2.5\ bar$

Therefore, the minimum pressure required is $2.5\ bar$.

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