A vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 1.00 atm at 20

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A vertical cylindrical tank contains 1.80 mol of an ideal...

A vertical cylindrical tank contains 1.80 $\mathrm{mol}$ of an ideal gas under a pressure of 1.00 atm at $20.0^{\circ} \mathrm{C}$ . The round part of the tank has a radius of $10.0 \mathrm{cm},$ and the gas is supporting a piston that can move up and down in the cylinder without friction. (a) What is the mass of this piston? (b) How tall is the column of gas that is supporting the piston?

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of a fixed amount (n) of an ideal gas using the gas constant (R). This concept is crucial when determining any one of these states of the gas if the other three are known, which is central to solving problems involving gases in a confined space, such as a gas-filled cylinder with a movable piston.

Piston Force Equilibrium

In a system where a piston is free to move without friction, the equilibrium condition requires that the force due to the gas pressure acting upward on the piston is balanced by the downward force due to the weight of the piston (and any additional load). This balance determines the pressure inside the cylinder that the gas must provide and is a key principle in connecting the mechanical forces to the gas’s state variables.

Cylindrical Geometry

Understanding the geometric properties of a cylinder is essential because the volume of the gas is directly related to the cylinder’s cross-sectional area and the height (or length) of the gas column, following the formula V = A × h. This relationship is used to determine the height of the gas column when the volume is known, linking the physical dimensions of the container with the state of the gas inside.

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