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At constant temperature , if pressure in...

At constant temperature , if pressure increases by 1% , the percentage decrease of volume is `:`

A

`1%`

B

`100 //101%`

C

`1//101%`

D

`1//100%`

Text Solution

Verified by Experts

The correct Answer is:
C

Let `P_(1) = 100` mm Hg
Increase in pressure
`= 100 xx ( 1)/( 100) = 1 `
`p_(2) = 100 +1 = 101 mm Hg `
`V_(1) = V` and `V_(2) = ?`
`p_(1) V_(1) = p _(2) V_(2)`
or `V_(2) = ( p_(1) V_(1))/(p_(2)) = ( 100 xx V )/( 101) = ( 100)/( 101) V `
Decrease in volume `= ( V - ( 100)/( 101) V )/( V )`
` = V ( 1 - (100)/( 101))/( V ) = ( 1)/( 101)%`
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