A liquid is used to make a mercury-type barometer, as...

A liquid is used to make a mercury-type barometer, as described in Section $13.2 .$ The barometer is intended for spacefaring astronauts. At the surface of the earth, the column of liquid rises to a height of 2185 $\mathrm{mm}$ , but on the surface of Planet $\mathrm{X},$ where the acceleration due to gravity is one-fourth of its value on earth, the column rises to only 725 $\mathrm{mm} .$ Find (a) the density of the liquid and (b) the atmospheric pressure at the surface of Planet $\mathrm{X}$ .

A liquid is used to make a mercury-type barometer, as described in Section $13.2 .$ The barometer is intended for spacefaring astronauts. At the surface of the earth, the column
of liquid rises to a height of 2185 $\mathrm{mm}$ , but on the surface of Planet $\mathrm{X},$ where the acceleration due to gravity is one-fourth of its value on earth, the column rises to only 725 $\mathrm{mm} .$ Find (a) the density of the liquid and (b) the atmospheric pressure at the surface of Planet $\mathrm{X}$ .

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Key Concepts

Hydrostatic Pressure

This concept involves the pressure exerted by a fluid at rest due to the force of gravity. It is expressed by the equation P = ?gh, where P is the pressure, ? is the fluid density, g is gravitational acceleration, and h is the height of the fluid column. It is fundamental for understanding how pressure builds up in a liquid column such as in barometric instruments.

Barometric Measurement

Barometers measure atmospheric pressure by comparing it to the hydrostatic pressure of a contained liquid column. In the case of a mercury-type barometer, the height of the liquid column equilibrates with the external atmospheric pressure, thus providing a direct indication of that pressure. This principle applies regardless of the specific liquid, provided its density is known.

Effect of Gravitational Variation

Gravitational acceleration is a critical factor in the relationship between the height of a liquid column and the pressure it exerts. When gravity is reduced, as on other planets, a different liquid column height is required to balance the same atmospheric pressure. This variation must be accounted for when applying hydrostatic principles in environments with gravity differing from that on Earth.

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