Q. At constant temperature, the volume of a gas is to be decreased by 4%. The pressure must be increased by

A) 4%
B) 4.16%
C) 8%
D) 3.86%
Explanation

(b) At constant temperature,
$p_{1}V_{1} = p_{2}V_{2}$
Or $\frac{p_{1}}{p_{2}} = \frac{V_{2}}{V_{1}}$
Fractional change in volume
$\frac{V_{1} - V_{2}}{V_{1}} = \frac{4}{100} = \frac{1}{25}$
$1 - \frac{V_{2}}{V_{1}} = \frac{1}{25}$
$\frac{V_{2}}{V_{1}} = \frac{24}{25}$
$\therefore\ \ \frac{p_{1}}{p_{2}} = \frac{V_{2}}{V_{1}} = \frac{24}{25}$
or $\frac{p_{2}}{p_{1}} = \frac{25}{24}$
$\frac{p_{2} - p_{1}}{p_{1}} = \frac{25}{24} - 1 = \frac{1}{24}$
% increase in pressure $= \frac{100}{24} = 4.16\%$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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