Answer to Question #114954 in Molecular Physics | Thermodynamics for Noma Msomi

Question

The 1.0-m-tall cylinder in FIGURE P14.61 contains air at a pressure of 1 atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?

Hint: Boyle’s law, which you learned in chemistry, says for a gas compressed at constant temperature, which we will assume to be the case.

Answer 1

Some of the assumptions taken before solving the question

1) piston is mass-less

2) piston is frictionless

3) the piston just fits the cylinder such that no air escapes from it and no heat is generated due to friction

here atmospheric pressure is equivalent to 76 cm of mercury level and 200 is the height of the column

here temperature being constant so we will apply boyle's law here

which says PV=constant

and here we will substitute V= height of fluid column$\times$cross-section area

For Boyle's law to hold

$P_1 ​V_1 ​=P_2 ​V_2 ​$

$76×A×200=(76+h)×A×(200−h)\\ 76×200=(76+h)(200−h)\\ 76×200=15200−76h+200h−h^2\\ h^2+124h−15200+15200=0\\ h^2=+124h\\ h=+124㎝$

Hence, height of piston=200−124

=76㎝