# By what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by 10%

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By  what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by 10% at a constant temperature?

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According to boyle's law

(P + ΔP) (V - ΔV) = PV

(P + ΔP) (V - 0.1 V) = PV

PV + VΔP - 0.1 PV - 0.1 VΔP = PV

0.9 V ΔP = 0.1 PV

$\frac{ΔP}{P}$ = $\frac{1}{9}$

Percentage increase = $\frac{ΔP}{P}$ x 100 = $\frac{100}{9}$ = 11.1

Percentage increase = 11.1 %

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