The pressure p and the volume V of a gas are connected by the relation, `pV^(1//4) = k`, where k is a contant. Find the percentage increase in the pressure, corresponding to a diminution of 0.5% in the volume

Answer

0.00125

Explanation

`pV^(1//4) = k rArr log p + (1)/(4) log V = log k`
`rArr (1)/(p).(dp)/(dV) + (1)/(4V) = 0 rArr (1)/(p).(dp)/(dV).delta V = - (1)/(4V) .deltaV`
`rArr (1)/(p).deltap = - (1)/(4V).deltaV rArr ((deltap)/(p) xx 100)`
`rArr ((deltap)/(p) xx 100) = - (1)/(4) ((deltaV)/(V) xx 100) = (-(1)/(4)) (-(1)/(2)) = (1)/(8)`