Calculating Cross-Sectional Area Using Boyle's Law and a Mercury Barometer

[ritwik06]

A mercury barometer reads 75 cm. Now 3 cc of atmospheric air is introduced into the tube. The mercury falls to a height of 65 cm and the length of air column above mercury is found to be 15 cm. Calculate the cross sectional area of the tube.
This question in my book has been solved by boyle's law.

... The mercury level falls to 65cm because air in the tube exerts pressure on it therefore pressure of air inside the tube =10cm of Hg...

10cm of Hg is the pressure which the air column exerts over mercury. Isnt it? Now how can we say that the air is at 10cm of Hg pressure. The pressure on air should be equal to the pressure exerted on it by the wall of the tube and the free mercury surface. Please explain!

 

[andrevdh]

The barometer balances pressure. The pressure on top of the surface of the mercury and the pressure of the column of mercury balances the atmospheric pressure at the base of the column. Inserting the initial 3 cc of air at atmospheric pressure will push the surface of the mercury down since the downwards pressure is now larger than the upwards pressure. This means that the air on top of the mercury will now expand and thereby decrease its pressure on top of the surface. This process will continue until the pressures balances again.

 

[ritwik06]

The barometer balances pressure. The pressure on top of the surface of the mercury and the pressure of the column of mercury balances the atmospheric pressure at the base of the column. Inserting the initial 3 cc of air at atmospheric pressure will push the surface of the mercury down since the downwards pressure is now larger than the upwards pressure. This means that the air on top of the mercury will now expand and thereby decrease its pressure on top of the surface. This process will continue until the pressures balances again.

I understand this! Thanks!

 

[andrevdh]

I am glad I could be of help to you.