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.

Answer 1

10.5 m

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

`rho_1h_1g = rho_2h_2g`

`h_2 = (rho_1h_1)/rho_2`

`= (13.6xx10^3xx0.76)/984`

= 10.5 m

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

Answer 2

We know that atmospheric pressure, `P = 1.01 xx 10^5 "Pa"`

If we use French wine of density,  `rho= 984 kg m^(-3)`, then height of wine column should be

`h_(m')` such that `p = hrhog`

`=> h_m = P/(rhog) = (1.01xx10^5)/(984xx9.8) = 10.47m ~~10.5 m`