When pressure increases by 2% , what is the percentage decrease in the volume of a gas, assuming Boyle's law is obeyed ?

Explanation

Let .P. be the initial pressure and .V. be the volume.
When pressure is increased by `2%`, new pressure , `P^(1) = P + 2/100 P implies P^(1) = 102/100P`
According to Boyle.s law, PV = constant
`implies PV = P.V.`
`implies PV = 102/100 P xx V. or V. = 100/102 V`
% decrease in volume = `(V-V.)/V xx 100`
`=((V-100/102V))/(V)xx100`
% decrease in volume = `2/102 xx 100 = 1.96%`
`:.` When pressure increased by 2% , the volume decrease by 1.96%.