The pressure P and volume V of a gas are connected by the relation `P V^(1/4=)` constant. The percentage increase in the pressure corresponding to a deminition of % in the volume is `1/2%` (b) `1/4%` (c) `1/8%` (d) none of these

Explanation

`pv^(1/4) = c`

`p= cv^(-1/4)`

`ln p = ln(cv^(-1/4))`

`ln p = ln c + (-1/4)ln v`

now, `(dp)/p = 0- 1/4(dv)/v`

`(dp)/p = -1/4 (dv)/v`

`(dp)/p = -1/4(-1/2%)`

`= 1/8%`

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