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.
Solution 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
Solution 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`
