please help me with this problem A vertical cylindrical tank contains 1.90 mol o

Question

please help me with this problem

A vertical cylindrical tank contains 1.90 mol of an ideal gas under a pressure of 0.500 atm at 20degree C. The round part of the tank has a radius of 10 cm. and the gas is supporting a piston that can move up and down in the cylinder without friction. There is a vacuum above the piston. What is the mass of this piston? Express your answer with the appropriate units. How tall is the column of gas that is supporting the piston? Express your answer with the appropriate units.

Explanation / Answer

(A) Piston is in equilibrium.

Hence Fnet = Pressure force - m g = 0

P A = m g

(0.500 x 101325) (pi x 0.10^2 ) = m x 9.8

m = 162.4 kg ...............Ans

(B) Applying P V = n R T

(0.50 x 101325) ( V) = (1.90) (8.314) ( 273 + 20)

V = 0.09136 m^3

and V = A h

0.09136 = (pi x 0.10^2 ) h

h = 2.91 m .......Ans

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