The piston of a vertical piston-cylinder device containing a...

The piston of a vertical piston-cylinder device containing a gas has a mass of $60 \mathrm{~kg}$ and a cross-sectional area of $0.04 \mathrm{~m}^{2}$, as shown in Fig. $\mathrm{P} 1-60 .$ The local atmospheric pressure is 0.97 bar, and the gravitational acceleration is $9.81 \mathrm{~m} / \mathrm{s}^{2}$. (a) Determine the pressure inside the cylinder. (b) If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?

The piston of a vertical piston-cylinder device containing a gas has a mass of $60 \mathrm{~kg}$ and a cross-sectional area of $0.04 \mathrm{~m}^{2}$, as shown in Fig. $\mathrm{P} 1-60 .$ The local atmospheric pressure is 0.97 bar, and the gravitational acceleration is $9.81 \mathrm{~m} / \mathrm{s}^{2}$.
(a) Determine the pressure inside the cylinder.
(b) If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?

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Key Concepts

Force Equilibrium

Force equilibrium is critical in systems where a movable boundary, such as a piston, is present. It means that the forces acting on the piston—such as its weight and the atmospheric pressure on one side, and the gas pressure on the other—must balance. This balance determines the internal pressure of the gas. Even with a change in the gas volume, if the forces remain the same, the pressure remains constant.

Isobaric Process

An isobaric process is one in which the pressure remains constant despite changes in volume. In the context of the problem, when heat is transferred to the gas causing it to expand, the piston moves to maintain the same force balance, thereby keeping the internal pressure unchanged. This concept is vital for understanding how heating can lead to volume changes without a corresponding change in pressure.

Hydrostatic Pressure

This concept involves the pressure exerted by a fluid (or in this case, the gas against the moving piston) due to the weight of an overlying column of material. In the problem, hydrostatic pressure is used to determine the pressure contributed by the piston weight acting on the area, which adds to the atmospheric pressure to maintain equilibrium.

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