The solution to this states that "pressure of the gas is constant." What implies this? Is it because the piston was elevated then stopped? If the gas pushed the Piston all the way up to where it stopped moving (and kept pushing) would Pressure be constant then? Thank You.
For the pressure of the gas to be considered constant, the expansion would have to be carried out quasistatically that is, very slowly, so that the pressure of the gas was only differentially greater than the external pressure at each stage of the expansion, or
$$P_{gas}=P_{ext}+dP$$
In this way the pressure of the gas can be considered in equilibrium with the external pressure throughout the expansion.
Hope this helps.
In this case, it's required for the piston to remain stationary in its new position.
If the piston isn't moving, this means that the net force on it is 0. If you look at the force balance on the piston, there are two forces that will be acting to move the piston vertically. The weight of the piston will be a downwards force, and the pressure difference between the cylinder and the surroundings will provide the upwards force.
We can then look at the formulas for the force due to weight, and force due to pressure: $$F_W = m g$$ and $$F_P = \Delta P A$$ therefore $$F_{\text{Net}} = F_W - F_P = mg - \Delta P A = 0$$
Knowing that the mass of the piston ($m$) doesn't change, and knowing that the area of the piston ($A$) doesn't change, you can see that $\Delta P$ cannot change if the piston is stationary in both positions, and no additional forces are introduced at equilibrium.
Pressure changes travel through the gas at the speed of sound. The question doesn't specify what gas is in the cylinder (because that is irrelevant to the question) but for air at sea level the speed of sound is about 1100 feet per second.
So if the piston moves by 1 foot, the pressure in the gas will even out in about 1 millisecond, and for practical purposes you can assume the pressure is always the same at every position in the cylinder.
