At constant temperature an increase in the pressure of a gas by 5% will decrease its volume by

Option 1 - 5%

Option 2 - 5.26%

Option 3 - 4.26%

Option 4 - 4.76%

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Answered by

Raj Pandey | Contributor-Level 9

4 months ago

Correct Option - 4

Detailed Solution:

If $P_{1} = P$ then $P_{2} = P + 5 %$ of $P = 1.05 P .$

From Boyle's law, $P V = constant$ therefore,

$\frac{V_{2}}{V_{1}} = \frac{P_{1}}{P_{2}} = \frac{P}{1.05 P} = \frac{100}{105}$

Fractional change in volume is

$\frac{Δ V}{V} = \frac{V_{2} - V_{1}}{V_{1}} = \frac{100 - 105}{105} = - \frac{5}{105}$

Therefore, percentage change in volume is

$\frac{Δ V}{V} * 100 % = - \frac{5}{105} * 100 % = - 4.76 %$

That is, volume decreases by $4.76 % .$

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