The percentage change in the pressure of a given mass of a gas filled in a container at constant temperature is $100$ %. Calculate the percentage change in its volume.

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Solution

The percentage change in the pressure of a given mass of a gas filled in a container at constant temperature $= 100 %$
Find the percentage change in its volume $= ?$
According to Charles and Boyle's law
$P V = c o n s t a n t$
If pressure increases, the volume decreases
$I n i t i a l p r e s s u r e F i n a l p r e s s u r e 100200 P ? (P_{1}) ∴ F i n a l p r e s s u r e = \frac{200 P}{100}$
$I f i n i t i a l v o l u m e = V$
$F i n a l v o l u m e = V_{1}$
$P V = P_{1} V_{1}$
$P \times V = \frac{200 P}{100} V_{1}$
$V_{1} = \frac{100 V}{200} V = \frac{1}{2} V V_{1} = \frac{1}{2} V ∴ P e r c e n t a g e c h a n g e = \frac{(V - V_{1}) \times 100}{V} = (\frac{V - \frac{1}{2} V}{2}) \times 100 = \frac{1 / 2 V}{V} \times 100 = \frac{1}{2} \times 50 %$
$= 50 %$ decreases

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