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Chapter 4: Problem 16

The way pressure increases with depth in a gas is different from the way it does in a liquid. Why?

Short Answer

Expert verified
Question: Compare the way pressure increases with depth in a gas and a liquid, considering their distinct properties and how they affect pressure behavior.

Step by step solution

01

Understanding pressure

Pressure is the force exerted on a given area. In the case of fluids (gases and liquids), it is caused by the weight of fluid above a particular point. As we go deeper into a fluid, the pressure increases due to the increasing weight of the fluid pushing down from above.
02

Recognizing the properties of gases and liquids

Gases and liquids have distinct properties that affect their pressure behavior. Gases are highly compressible and have variable densities, whereas liquids are relatively incompressible and have more or less constant densities. It means that the pressure in a gas can change significantly with changes in volume, while pressure in a liquid remains more constant.
03

Relating pressure to depth in a gas

In a gas, the pressure increase with depth is affected significantly by its compressibility. As the pressure increases due to the weight of the gas above, the gas compresses, changing its density. Thus, a greater depth in a gas may result in more significant pressure difference than in a liquid, as a more massive amount of gas will be pressing down. Moreover, temperature and pressure variations in a gas also cause its density to change more with depth.
04

Relating pressure to depth in a liquid

In a liquid, the pressure increases directly with depth mainly due to the weight of the liquid above it, as liquids are nearly incompressible, and their density remains constant regardless of the pressure applied. Therefore, the pressure increase with depth in a liquid tends to be more straightforward and is not significantly affected by changes in temperature or pressure.
05

Comparison between gas and liquid

In summary, the way pressure increases with depth in a gas is different from a liquid due to their properties. Gases are compressible with variable densities while liquids are incompressible with constant densities. Therefore, pressure in a gas is more sensitive to volume changes and temperature variations than in a liquid, causing a more significant or less predictable pressure increase with depth in a gas than in a liquid.

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