A faulty barometer tube is `90cm` long and its contains some air above mercury. The reading is cm when the true atmospheric pressure `76cm`. What will be the true atmospheric pressure if the reading on this barometer is 74 cm? (H = 10cm of water column)

Explanation

Let the area of cross-sectional of the tube `A_(cm)^(2)` and the true pressure be `H cm` of mercury. Since the temperature is constant., Boyle's law can be applied to the air enclosed in the upper part of the barometer tube, thus
`P_(1) = (76.0 - 74.5) = 1.5cm` of mercury
`V_(1) = A xx (90 - 74.5) = A xx 15.5cm^(3)`
`P_(2) = (H - 74.0) cm` of mercury
`V_(2) = A xx (90 - 74.0) = A xx 16cm^(3)`
Applying Boyle's law `P_(1)V_(1) = P_(2)V_(2)`
`1.5 xx (A xx 15.5) = (H - 74) xx (A xx 16)`
`H - 74 = (1.5 xx 15.5)/(16)`
`H = 75.45cm`