How much should the pressure be increased in order to decrease the volume of a gas by 5% at constant temperature

25%

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10%

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4.26%

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5.26%

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Solution

The correct option is
D

5.26%
When the temperature is constant then apply Boyles Law
$P_{1} V_{1} = P_{2} V_{2}$
$V_{2} = 0.95 V_{1} (A s V_{2} 0.5 % l e s s t h a n V_{1})$
$P_{1} V_{1} = P_{2} \times 0.95 V_{1}$

$P_{1} = \frac{P_{2} \times 0.95 V_{1}}{V_{1}}$
$P_{2} = \frac{P_{1}}{0.95} = 1.052 p_{1}$
% Increase in pressure = $\frac{f i n a l p r e s s u r e - i n i t i a l p r e s s u r e}{i n i t i a l p r e s s u r e} \times 100$
% Increase in pressure=
$\frac{1.052 P_{1} - P_{1}}{P_{1}}$
=
$\frac{P_{1} (1.052 - 1)}{P_{1}}$
=
$0.052 \times 100$

=5.26%

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