Question

This is a 3-part question

1; If the column of water in the water barometer rose to a height of 34 feet, what would the atmospheric pressure be in mm Hg?

2; Explain the Boyle's Law relationship. What kind of apparatus did Boyle use to determine that relationship.

3; Given a column of air with a pressure of 1.57 x 10⁵ Pa and an area of 1.13 m² and given that the acceleration due to gravity is 9.8 m/s², what is the mass of this column?

Answer 1

1) Given , 34 feet(ft) water
We know,

1ft=12 inch

1inch =25.4 mm

and 1 mm Hg=13.6 mm H2O

34 ft H₂O x (12 in H₂O/1ft H₂O)x (25.4 mm H2O/1in H₂O)x (1mm Hg/13.6 mm H₂O)

= (10363.2 / 13.6) mm Hg

= 762 mm Hg

2) Boyle's law--> It is the pressure-volume relationship of a given mass of gas at constant temperature and first stated by Robert Boyle.

The law states that at constant temperature the volume of a given mass of gas is inversely proportional to its pressure.

i.e. V 1 /P => V = k /P => PV = k , k = proportionality constant

Robert Boyle demonstrated this relationship with the help of a U-shaped tube that was sealed at one end. The tube contained mercury which was added to it so that the volume of gas was trapped at the sealed end of the tube. As a result, the gas was compressed by atmospheric pressure and the pressure from the mercury column. Also, Boyle poured mercury into the open end of the U-tube and calculated the change in volume of the gas that was trapped as the applied pressure increased.

3) Given, P = 1.57 x 10⁵ Pa= 157000 N/ m², Area = 1.13 m² , g = 9.8 m/s²

We know, P = F/ A

Also, P = W / A

=> W = P x A

=> W = ( 157,000 N. / m². )x ( 1.13 m² ) = 1747410 N.

From, Newton's second law of motion,

W = mg

=> m = W / g

=> m = 1747410 N / 9.8 m/s²

=> m = 178307 kg

2) Boyle's law--> It is the pressure-volume relationship of a given mass of gas at constant temperature and first stated by Robert Boyle.

The law states that at constant temperature the volume of a given mass of gas is inversely proportional to its pressure.

i.e. V 1 /P => V = k /P => PV = k , k = proportionality constant

Robert Boyle demonstrated this relationship with the help of a U-shaped tube that was sealed at one end. The tube contained mercury which was added to it so that the volume of gas was trapped at the sealed end of the tube. As a result, the gas was compressed by atmospheric pressure and the pressure from the mercury column. Also, Boyle poured mercury into the open end of the U-tube and calculated the change in volume of the gas that was trapped as the applied pressure increased.