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

How much should the Pressure be increased in order to decrease

A
5%
B
5.26 %
C
10%
D
4.26%

Solution:

If $V_{i} = V_{1}, then, V_{2} = V_{1} - \frac{5}{100} \times V_{1} = \frac{95 V_{1}}{100}$
Let initial pressure be P₁ and final pressure be P₂
$∴$ Applying Boyle's law, $P_{1} V_{1} = P_{2} V_{2}$
or $\frac{P_{1}}{P_{2}} = \frac{V_{2}}{V_{1}} = \frac{\frac{95 V_{1}}{100}}{V_{1}} = \frac{95}{100}$
Percentage increase in pressure = $\frac{P_{2} - P_{1}}{P_{1}} \times 100 = (\frac{P_{2}}{P_{1}} - 1) \times 100$
$∵ \frac{P_{2}}{P_{1}} = \frac{100}{95}$
$∴$ Percentage increase in pressure = $(\frac{100}{95} - 1) \times 100 = \frac{5}{95} \times 100 = \frac{500}{95} = 5.26 %$

Solution:

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