Question

The cylinder above contains an ideal gas and has a movable, frictionless piston of diameter D and mass M. The cylinder is in a laboratory with atmospheric pressure Patm. Express all algebraic answers in terms of the given quantities and fundamental constants.

a. Initially, the piston is free to move but remains in equilibrium.
i. The force that the confined gas exerts on the piston
ii. The absolute pressure of the confined gas
b. If a net amount of heat is transferred to the confined gas when the piston is fixed, what happens to the pressure of the gas?

Answer 1

The force exerted by an ideal gas on a piston in equilibrium can be calculated from pressure and area. If heat is added to a contained gas with a fixed volume, the pressure increases due to the increased molecular kinetic energy.

Step-by-step explanation:

The question pertains to a scenario involving a cylinder with a movable piston, which contains an ideal gas subjected to certain conditions. When the piston is in equilibrium, the force exerted by the gas on the piston can be calculated by using the atmospheric pressure and the area of the piston. The absolute pressure of the confined gas equals the atmospheric pressure plus the pressure contributed by the weight of the piston. The force exerted by the gas is the product of the pressure of the gas and the cross-sectional area of the piston.

Regarding part (b) of the question, if heat is transferred to the confined gas while the piston is fixed, the pressure of the gas will increase. This is due to the fact that adding heat to the system increases the kinetic energy of the gas molecules, resulting in greater pressure if the volume is kept constant.