A 100 cm long vertical cylinder,closed at the bottom end , has a movable,frictionless,air tight disattached at its other end. An ideal gas is confined within the cylinder. Initially when the disc between the confined gas and atmosphere is in equilibrium,the length of the gas column is 90 cm. Mercury is poured slowly on the disc. When the disc descends by 32 cm,mercury over it is just about to overflow. Find the atmospheric pressure if the operation took place at a constant temperature of the gas. Neglect the weight or thickness of the disc.

A 100 cm long vertical cylinder,closed at the bottom end , has a movab

1.	A 100 cm long vertical cylinder,closed at the bottom end , has a movable,frictionless,air tight disattached at its other end. An ideal gas is confined within the cylinder. Initially when the disc between the confined gas and atmosphere is in equilibrium,the length of the gas column is 90 cm. Mercury is poured slowly on the disc. When the disc descends by 32 cm,mercury over it is just about to overflow. Find the atmospheric pressure if the operation took place at a constant temperature of the gas. Neglect the weight or thickness of the disc.
Answer» SOLUTION :Let the atmospheric pressure be p cmHg and a=area of cross SECTION of the cylinder. Initially in equilibrium, pressure of confined gas = atmospheric pressure p. Now, volume of enclosed gas `V=90a CM^3` When mercury just overflows from the cylinder,pressure of the gas `p_1=(p+42)` cmHg (Fig.6.4) and volume `V_1=(90-32)a=58a cm^3`. As the temperature is constant,according to Boyle.s law `pV=p_1V_1` or, `p times 90 a=(p+42)times 58a` `90p=58p+58 times 42` or,`32 p=58 times 42` or, `p=(58 times 42)/32=76.125 cm Hg`