A cylindrical container contains a light (so that you can neglect its weight), a

Question

A cylindrical container contains a light (so that you can neglect its weight), airtight piston that can move up and down the inside of the cylinder. The radius of the piston is 15 cm. The temperature of the air in the piston is 20 degree C. When the system of the piston, cylinder and air inside the cylinder has reached equilibrium, the piston is 20 cm above the base of the cylinder. (a) How many moles of gas are inside the cylinder? (b) The cylinder is to the submerged in water at a depth where the pressure is 1.5 atm. How deep must the cylinder be? (c) When the cylinder is submerged at the depth you found in part (b). what is the height of the piston above the base of the cylinder?

Explanation / Answer

part a:

pressure =1 atm=101325 N/m^2

temperature=20 degree celcius=273+20=293 K

volume=pi*radius^2*height

=pi*0.15^2*0.2
=0.014137 m^3

then number of moles=pressure*volume/(gas constant*temperature)

=101325*0.014137/(8.314*293)

=0.588

part b:

gause temperature=density of water*g*depth

==>1.5 atm -1 atm=1000*9.8*depth

==>depth=0.5*101325 N/m^2/(9.8*1000)

=5.1696 m

part c:

let height of piston from the base of cylinder be h meters.

then pressure*volume=number of moles*gas constant*temperature

==>voulme=0.588*8.314*293/(1.5*101325)

==>pi*0.15^2*h= 0.0094243

==>h=0.1333 m

height of the piston is 13.33 cm

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