In order to increase the volume of a gas by `10%` , the pressure of the gas should be

Options

A. decreased by `1%`
B. decreased by `10%`
C. increased by `10%`
D. increased by `1%`

Answer

B

Explanation

According to Boyle's law ,
`p prop (1)/(V)`
Thus , if the volume is increased by `10%` , the pressure should decreases by `10%`.
According to Boyle's law ,
`p_(1)V_(1) = p_(2)V_(2)`
`V_(2) = V_(1) + (10)/(100) V_(1) = V_(1) + (V_(1))/(10) = (11)/(10) V_(1)`
`:. p_(1)V_(1) = p_(2)((11)/(10)V_(1))`
`p_(1) = (p_(2)11)/(10)`
or `p_(2) = (10)/(11) p_(1) = 0.9 p_(1) = 90% of p_(1)`
Thus , pressure is decrease by `10%`.