Thermodynamics problem?

Question

This is problem one on my worksheet, and all the rest I've found to be easy, 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.

How can you guys assume its at rest?

Answer 1

Calculate the pressure of the gas within the cylinder. This pressure acts as the 'upward' force acting on the piston.

Since we assume that the piston is at rest (no acceleration, no velocity), the 'downward' forces must cancel out the 'upward' forces.

The downward forces are provided from both the weight of the piston as well as the atmospheric pressure above the piston.
You know the atmospheric pressure, so you can subtract this off of the internal cylinder pressure. From this, you need to calculate the mass of the piston required to balance the internal pressure.


EDIT:
I think we can assume the cylinder is at rest because we are not told otherwise. In these types of problems you have to learn to make assumptions as to conditions which might not be explicitly stated. By assuming not only that the net force is zero (no acceleration), but also that the piston is at rest, it simplifies the problem. The question specifies that the air within the cylinder is at a given temperature, volume and pressure...it does not however say anything about these values changing with time as would be the case if the piston was moving/accelerating. The question also gives no indication that the piston is capable of being 'driven' in any way as a real piston in a car engine would so we have all the more reason to assume that the piston is only effected by the air pressure acting on it and its own weight.

Answer 2

I think they mean that the mass from the piston is counterbalancing the pressure, so that the piston is still. acceleration=0.