A vertical frictionless piston-cylinder device contains nitrogen at 125 kPa. The

Question

A vertical frictionless piston-cylinder device contains nitrogen at 125 kPa. The outside atmospheric pressure is 100kPa. The piston diameter is 25 cm. Use standard gravitational acceleration, determine:

(a) the mass of the piston in kg.

(b) the height difference between the two columns of mercury manometer (in cm), connected to the side of the cylinder, measure gas pressure in the cylinder. the density of mercury is 136000 kg/m^3. the density of the nitrogen is negligible compared to the density of mercury.

Explanation / Answer

(a)

mg/A = delta P

or, m = delta P * A / g

or, m = (125000 - 100000)* (pi * 0.1252) / 9.81

or, m = 125.14 kg

(b)

rho * g * h = delta P

or, h = delta P / rho * g

or, h = 125000-100000 / 136000 * 9.81

or, h = 0.0187 m

or, h = 1.87 cm

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