The Liquid Phase Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 5, 2011

Liquid Or Solid?

There is not always a defined answer to the question, “Is this substance a solid or a liquid?” It can depend on the observer’s point of reference. Some substances can be considered solid in the short-term time sense but liquid in the long-term sense. An example is the mantle of the Earth, the layer of rock between the crust and the core. In a long-term time sense, pieces of the crust, known as tectonic plates , float around on top of the mantle like scum on the surface of a hot vat of liquid. This is manifested as continental drift and is apparent when the Earth is evaluated over periods of millions of years. From one moment (as we perceive it) to the next, however, and even from hour to hour or from day to day, the crust seems rigidly fixed on the mantle. The mantle behaves like a solid in the short-term sense but like a liquid in the long-term sense.

Imagine that we could turn ourselves into creatures whose life spans were measured in trillions (units of 1012) of years so that 1 million years seemed to pass like a moment. Then, from our point of view, Earth’s mantle would behave like a liquid with low viscosity, just as water seems to us in our actual state of time awareness. If we could become creatures whose entire lives lasted only a tiny fraction of a second, then liquid water would seem to take eons to get out of a glass tipped on its side, and we would conelude that this substance was solid, or a else a liquid with extremely high viscosity.

The way we define the state of a substance can depend on the temperature, and it also can depend on the time frame over which the substance is observed.

Density Of Liquids

The density of a liquid is defined in three ways: mass density, weight density , and particle density . The difference between these quantities might seem theoretically subtle, but in practical situations, the difference becomes apparent.

Mass density is defined in terms of the number of kilograms per meter cubed (kg/m 3 ) in a sample of liquid. Weight density is defined in newtons per meter cubed (N/m 3 ) and is equal to the mass density multiplied by the acceleration in meters per second squared (m/s 2 ) to which the sample is subjected. Particle density is defined as the number of moles of atoms per meter cubed (mol/m 3 ), where 1 mol ≈ 6.02 × 10 23 .

Let d m be the mass density of a liquid sample (in kilograms per meter cubed), let d w be the weight density (in newtons per meter cubed), and let d p be the particle density (in moles per meter cubed). Let m represent the mass of the sample (in kilograms), let V represent the volume of the sample (in meters cubed), and let N represent the number of moles of atoms in the sample. Let a be the acceleration (in meters per second squared) to which the sample is subjected. Then the following equations hold:

d m = m/V

d w = ma/V

d p = N/V

Alternative definitions for mass density, weight density, and particle density use the liter , which is equal to a thousand centimeters cubed (1000 cm 3 ) or one-thousandth of a meter cubed (0.001 m 3 ), as the standard unit of volume. Once in awhile you’ll see the centimeter cubed (cm 3 ), also known as the milliliter because it is equal to 0.001 liter, used as the standard unit of volume.

These are simplified definitions because they assume that the density of the liquid is uniform throughout the sample.

Density of Liquids Practice Problems

Problem 1

A sample of liquid measures 0.275 m 3 . Its mass is 300 kg. What is its mass density in kilograms per meter cubed?

Solution 1

This is straightforward because the input quantities are already given in SI. There is no need for us to convert from grams to kilograms, from milliliters to meters cubed, or anything like that. We can simply divide the mass by the volume:

d m = m/V

= 300 kg/0.275 m 3

= 1090 kg/m 3

We’re entitled to go to three significant figures here because our input numbers are both given to three significant figures.

Problem 2

Given that the acceleration of gravity at the Earth’s surface is 9.81 m/s 2 , what is the weight density of the sample of liquid described in Problem 1?

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