What Is the Mass of the Piston in a Vertical Cylinder with Air at 100C?

[seang]

This is problem one on my worksheet, and all the rest I've found to be easier, so I'm thinking I'm missing something here:

A vertical cylinder fitted with a frictionless piston contains air at 100C The piston has an unknown m and a diameter of .150mm, and the ambient pressure outside the cylinder is 101kPa. If the cylinder volume is 500 liters and the mass of the air is 5kg, what is the piston mass, m?

I calculated the pressure inside the cylinder and it is huge. That means the piston would accelerate upwards. Since the sum of the forces on the piston must equal its mass times acceleration, I used something like (AFTER i had obtained the inner pressure):

p(sys)*a(piston) - p(ambient)*a(piston) - mass(piston)*gravity = mass(piston)*acceleration(piston)

The trouble is, is that i know neither the acceleration or the mass of the piston. THe only way this can work is if I assume that the piston is not moving, but I don't think I can just assume that?

 

[Andrew Mason]

This is problem one on my worksheet, and all the rest I've found to be easier, so I'm thinking I'm missing something here:

A vertical cylinder fitted with a frictionless piston contains air at 100C The piston has an unknown m and a diameter of .150mm, and the ambient pressure outside the cylinder is 101kPa. If the cylinder volume is 500 liters and the mass of the air is 5kg, what is the piston mass, m?

I calculated the pressure inside the cylinder and it is huge. That means the piston would accelerate upwards. Since the sum of the forces on the piston must equal its mass times acceleration, I used something like (AFTER i had obtained the inner pressure):

p(sys)*a(piston) - p(ambient)*a(piston) - mass(piston)*gravity = mass(piston)*acceleration(piston)

The trouble is, is that i know neither the acceleration or the mass of the piston. THe only way this can work is if I assume that the piston is not moving, but I don't think I can just assume that?

I don't see anything that suggests it is moving so assume it is at rest. What is the force on the piston at rest? So the weight + atmospheric pressure x area has to equal the pressure inside the cylinder x area. The key is figuring out the pressure inside the cylinder. Show us how you are calculating that.

Note: the area of the cylinder must be .150 m, not .150 mm.

AM

 

[seang]

Using Ideal gas law: Psys = ((5kg)(287J)(373K))/.5m^3

 

[andrevdh]

The idea is to assume that the piston is in equilibrium. The piston experiences three forces:

its weight downwards $W$
the downwards force on it due to atmospheric pressure pushing on it $p_a$
and the upwards force due to the pressure of the air inside of it $p_i$

these three forces need to cancel out.