Rank the following based off of the height of the liquid in the column at the unique conditions listed.

Question

In a barometer, the atmospheric pressure pushes mercury from a pool up a long tube while gravity pulls the mercury down. At average atmospheric pressure, the mercury is pushed up the column 760 mm (see figure). Pressure is often expressed in related units where 1 atm = 760 mmHg. 1 torr = 1 mmHg in honor of Evangelista Torricelli, who invented the barometer.

 Hg Barometer at 1.2 atm, Hg barometer at 1 atm, water barometer at 1 atm, water barometer at 0.8 atm, Hg barometer at 0.4 atm

Answer 1

P = ρ g h, where P is pressure, ρ is density of the fluid in the column, and g is the acceleration due to gravity. Solve for h.

P/(ρ G) = h

ρ of Hg is 5.43 g/ml = 5430 kg/m³

ρ of H₂O is 1 g/ml = 1000 kg/m³

G = 9.8 m/s²

(5) Hg Barometer at 1.2 atm, h = 1.2/5.43/G = .23/G (lowest column of fluid)

(4) Hg barometer at 1 atm, h = 1/5.43/G = ..18/G

(1) water barometer at 1 atm, h = 1/1.0/G = 1/g (highest column of fluid)

(2) water barometer at 0.8 atm, h = .8/1.0/G = ..8/G

(3) Hg barometer at 0.4 atm. h = .4/1.0/G = ..4/G

These are ranked in magnitude on the left. Since g is a constant, the larger the numerator, the larger the column rises. Use the conversion below to get the answer in meters.

P (Pa)= ρ (kg/m³) G (m/s²) h (m)

P (atm)*101325 = ρ (kg/m³) G (m/s²) h (m), so

h(m) = P (atm)*101325 / (ρ (kg/m³) * G (m/s²) )