A faulty barometer contains certain amount of air and saturated water vapour. It reads 74.0 cm when the atmospheric pressure is 76.0 cm of mercury and reads 72.10 cm when the atmospheric pressure is 74.0 cm of mercury. Saturation vapour pressure at the air temperature = 1.0 cm of mercury. Find the length of the barometer tube above the mercury level in the reservoir.

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Solution

Let the barometer has a length = X

Height of air above the air mercury column

= (X - 74 + 1) = (X-73)

Pressure of air = 76-74-1 = 1 cm
for 2nd case, height of air above

$\Rightarrow$ (X-72.1+1) = (X-71.1)
pressure of air = (74-72.1-1)= 0.90

(X-73) (1) = $\frac{9}{10}$ (X-71.1)

$\Rightarrow X = 10 \times 73 - 9 (71.1)$

= 730 - 639.9

X= 90.1

Height of air = 90.1

Height of barometer tube above the mercury column

= 90.1+1 = 91.1 mm

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