When pressure increases by 1%, what is the percentage decrease in… - Vidyadip

Question

When pressure increases by 1%, what is the percentage decrease in the volume of a gas, if Boyle's law is obeyed?

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Answer

We know PV = constant

If P is increased by 1%, then volume will decrease.

$\therefore$ (P + 0.01P)(V - dV) = PV

-PdV + 0.01PV - 0.01PdV = 0

-PdV(1 + 0.01) = -0.01PV

$\therefore\frac{\text{dV}}{\text{V}}=\frac{0.01}{1.01}$

% variation in volume = 0.98

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