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 the volume of a gas by 5% at a constant temperature?

1. A

5%

2. B

5.26 %

3. C

10%

4. D

4.26%

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+91

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### Solution:

If
Let initial pressure be P1 and final pressure be P2
$\therefore$ Applying Boyle's law, ${\mathrm{P}}_{1}{\mathrm{V}}_{1}={\mathrm{P}}_{2}{\mathrm{V}}_{2}$
or  $\frac{{\mathrm{P}}_{1}}{{\mathrm{P}}_{2}}=\frac{{\mathrm{V}}_{2}}{{\mathrm{V}}_{1}}=\frac{\frac{95{\mathrm{V}}_{1}}{100}}{{\mathrm{V}}_{1}}=\frac{95}{100}$
Percentage increase in pressure = $\frac{{\mathrm{P}}_{2}-{\mathrm{P}}_{1}}{{\mathrm{P}}_{1}}×100=\left(\frac{{\mathrm{P}}_{2}}{{\mathrm{P}}_{1}}-1\right)×100$

$\therefore$Percentage increase in pressure =$\left(\frac{100}{95}-1\right)×100=\frac{5}{95}×100=\frac{500}{95}=5.26%$  +91

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