Torricelli, who invented the barometer, used mercury inits construction because mercury has a very high density,which makes it possible to make a more compact barometerthan one based on a less dense fluid. Calculate the densityof mercury using the observation that the column ofmercury is 760 mm high when the atmospheric pressure is1.01 * 105 Pa. Assume the tube containing the mercury isa cylinder with a constant cross-sectional area.

Verified step by step guidance

Step 1: Understand that the pressure at the base of a fluid column is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

Step 2: In this problem, we are given P (atmospheric pressure = 1.01 * 10^5 Pa), g (acceleration due to gravity = 9.8 m/s^2), and h (height of the mercury column = 760 mm = 0.76 m). We are asked to solve for ρ (density of mercury).

Step 3: Rearrange the equation P = ρgh to solve for ρ. The rearranged equation is ρ = P / (gh).

Step 4: Substitute the given values into the rearranged equation. ρ = (1.01 * 10^5 Pa) / (9.8 m/s^2 * 0.76 m).

Step 5: Calculate the density of mercury by performing the division in the equation from step 4. This will give you the density of mercury in kg/m^3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It is a fundamental property of materials that influences how substances behave under various conditions. In the context of the barometer, the high density of mercury allows for a shorter column height compared to less dense fluids, making it practical for measuring atmospheric pressure.

Atmospheric Pressure

Atmospheric pressure is the force exerted by the weight of the air above a given point, measured in pascals (Pa) or millimeters of mercury (mmHg). At sea level, standard atmospheric pressure is approximately 101,325 Pa, which corresponds to a mercury column height of 760 mm. This relationship is crucial for understanding how barometers function, as they measure changes in atmospheric pressure by the height of the mercury column.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It is calculated using the formula P = ρgh, where P is the pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column. In the case of the barometer, the hydrostatic pressure of the mercury column balances the atmospheric pressure, allowing for the calculation of mercury's density based on the height of the column.

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