Problem #1: As shown in the diagram below, a gas is contained in a piston-cylind

Question

Problem #1:
As shown in the diagram below, a gas is contained in a piston-cylinder assembly. The piston
mass and cross-sectional area are denoted m and A, respectively. The only force acting on the top
of the piston is due to atmospheric pressure, patm. Assuming the piston moves smoothly in the
cylinder and the local acceleration of gravity (g) is constant, perform the following:
(a) Show that the pressure of the gas acting on the bottom of the piston remains constant as the
gas volume varies.
(b) Suggest something that could cause the gas volume to vary under these circumstances

Explanation / Answer

1.Considering the initial equilibrium of the piston.

P(gas)* A = Patm * A + mg

now, P atm and mg are invariant. They will not change.

As, it is said that , the piston moves smoothly in the cylinder. It can be assumed that , velocity of piston is constant.

Hence, net force accross the piston is still zero. As the force above the piston is not changed(  Patm * A + mg ), the force beneath the piston must also remain the same to maintain equilibrium.

hence,

pressure beneath the piston is still Pg.

2. Assuming it to be an isobaric process.(in which pressure is considered to be constant).

for those process, work is done due to heat input and internal energy change.

So , in order to increase the volume of the gas, we can increase the inside temperature and input some heat . Inside temperature and heat input van be done by making the walls of the cylinder non-adiabatic and increasing the outside temperature.

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