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States Of Matter

Question
CBSEENCH11005896

What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30C?

Solution

From the given data,
straight V subscript 1 space equals space 500 space dm cubed comma space space space straight P subscript 1 space equals space 1 space bar
straight V subscript 2 space equals space 200 space dm cubed comma space space straight P subscript 2 space equals space ?
According to Boyle's law,
                   straight P subscript 1 straight V subscript 1 space equals space straight P subscript 2 straight V subscript 2
or space space space straight P subscript 2 over straight P subscript 1 space equals space straight V subscript 1 over straight V subscript 2
Substituting the values, we have,
   fraction numerator straight P subscript 2 over denominator 1 space bar end fraction space equals space fraction numerator 500 space dm cubed over denominator 200 space dm cubed end fraction
therefore space space space fraction numerator straight P subscript 2 over denominator 1 space bar end fraction space equals space 2.5
or space space space space space straight P subscript 2 space equals space 2.5 space bar