Question

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 kg m–3. Determine the height of the wine column for normal atmospheric pressure.
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Answer 1

$\huge \sf{solution}$

Density of mercury, ρ1 = 13.6 × 103 kg/m3

Height of the mercury column, h1 = 0.76 m

Density of French wine, ρ2 = 984 kg/m3

Height of the French wine column = h2

Acceleration due to gravity, g = 9.8 m/s2

The pressure in both the columns is equal, i.e.,

Pressure in the mercury column = Pressure in the French wine column

ρ1h1g = ρ2h2g

h2 = ρ1h1 / ρ2

= 13.6 × 103 × 0.76 / 984 = 10.5 m

Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m.

Answer 2

Explanation:

Density of mercury, ρ1 = 13.6 × 103 kg/m3

Height of the mercury column, h1 = 0.76 m

Density of French wine, ρ2 = 984 kg/m3

Height of the French wine column = h2

Acceleration due to gravity, g = 9.8 m/s2

The pressure in both the columns is equal, i.e.,

Pressure in the mercury column = Pressure in the French wine column

ρ1h1g = ρ2h2g

h2 = ρ1h1 / ρ2

= 13.6 × 103 × 0.76 / 984 = 10.5 m

Hence, the height of the French wine column for normal atmospheric pressure is 10.5 m.