The concept of density

In physics, the mass per unit volume of a substance is called its density.

1, the ratio of the mass of a substance to its volume, that is, the mass of the substance in unit volume, is called the density of this substance. Sign ρ. The main international unit is kg/m 3, and the common unit is g/cm 3.

Its mathematical expression is ρ = m/v. In the international system of units, the main unit of mass is kilogram and the main unit of volume is cubic meter, so the mass of 1 cubic meter is taken as the density of matter. For heterogeneous materials, it is called "average density".

2. The physical meaning of density. Taking water as an example, the density of water at 4℃ is 10 3kg/m 3 or1g/cm3 (1.0×103kg/m3). The physical meaning is that the mass of water per cubic meter is 1.0×.

The average density of the earth is 5.5×10.3 kg/m3.

The average density of dry air under standard conditions is 0.001.293×10.3 kg/m 3.

Density of common nonmetallic solids, metals, liquids and gases: (unit: kg/m 3) Gold: 19.3× 10 3 Silver: 10.5× 10 3 Steel: 7.9× 65438+.

Lead: 1 1.3× 10 3 copper: 8.9× 10 3 aluminum: 2.7× 10 3 dry pine: 0.5× 10 3 mercury: 65438+.

Kerosene, alcohol 0.8× 10 3 gasoline: 0.7 1× 10 3 carbon dioxide: 1.98 oxygen: 1.43 air: 1.29 carbon monoxide:/kloc-.

3. It refers to the mass number of substances contained in a unit volume at a specified temperature, expressed in kg/m 3 (in kilograms per cubic meter) or g/cm 3 (in grams per cubic centimeter). It is mainly used for the measurement of conversion quantity and delivery acceptance, the quality control of some oil products and the simple judgment of oil products' performance.

4. In printing terms, reflection density refers to the shading ability of the surface; Transmission density refers to the shading ability of the filter.

5. The density of photosensitive material refers to the degree of image depth after exposure and development. Such as film, the more transparent the picture, the smaller the density; On the contrary, the more opaque the place, the greater the density.

Density is a physical quantity that reflects the characteristics of matter, and the characteristics of matter refer to a property that can be distinguished from each other. People often think that substances with high density are "heavy" and substances with low density are "light". The "heavy" and "light" here essentially refer to the size of density.

Mass is the quantity of matter contained in an object. The substance content decreases, so the mass decreases. Density is a characteristic of a substance, which does not change with the change of mass and volume, and the density of the same substance remains unchanged.

Density is a characteristic of matter, which is only related to the type of matter, and has nothing to do with factors such as mass and volume. Different substances generally have different densities, while the density of the same substance is the same.

The formula of density: ρ = m/v (ρ means density, m means mass and v means volume).

When we correctly understand the density formula, we should pay attention to the conditions and special meanings expressed by various physical quantities. From a mathematical point of view, there are three situations:

(1) ρ is certain, and m is proportional to v;

(2) When m is constant, ρ is inversely proportional to V;

(3) When V is constant, ρ is proportional to m. ..

Combined with the physical meaning, only (1) is correct, and (2) and (3) are wrong. Because the density of the same substance is constant and does not change with the change of volume and mass, we can't understand the physical formula without physical facts, nor can we simply understand the relationship between the quantities in the physical formula from a mathematical point of view.

5. The density unit in the international system of units is: kg/m3. The correct pronunciation is kilograms per cubic meter, and the symbol is kg/m3. The common unit is gram/cubic centimeter. The correct pronunciation is grams per cubic centimeter, and the symbol is g/cm3.

The transformation relationship between them:

1 g/cm3 = 1000 kg/m3

6. The density of water is 1000 kg/m3.

Its physical meaning is that the volume is 1 m3 and the mass of water is 1000kg.

7. According to the change of density formula: m=vρ or v=m/ρ, the mass and volume of an object can be calculated, especially some problems that are inconvenient for direct measurement, such as calculating the volume of irregular objects and the mass of historic sites. Density is one of the characteristics of matter. Every substance has a certain density, and the density of different substances is generally different. So we can use density to identify substances. The method is to measure the density of the measured substance, and compare the measured density with the density of various substances in the density table, so as to identify what substances the object is made of.

8. Use density knowledge to solve simple problems, such as judging whether an object is hollow or not, and use "analysis method" to solve some more complicated problems.

There are usually three ways to determine whether an object is hollow or solid:

(1) Calculate its density according to the formula, and then compare it with the density ρ of matter, if >: ρ, it is hollow; If = ρ, it is a solid.

(2) Given the mass, calculate V from the formula V = m/ρ, and then compare with V. If V >；; V is hollow; If V=V, it is a solid.

(3) treat the object as a solid object, use it to find the mass of a solid object with a volume of V, and then compare M with the actual mass of the object. If m >；; M, the object is hollow; If m=m, the object is solid.

9. The density of human body is only 1.07g/cm3, which is only a little more than water. It shouldn't be too difficult to learn swimming! Gasoline is less dense than water, so you know why all the oil stains you see on the road float on the water. The density of seawater is greater than that of water, so the human body is more likely to float in seawater.

The density of water is actually greater than that of ice. Why don't you get some ice cubes from the refrigerator and throw them into half a glass of water to see if the ice cubes are floating? Or sink. The density of a substance will change under the influence of temperature. Generally speaking, the quality of a substance is not affected by temperature, but its volume will expand with heat and contract with cold. So when the temperature rises, the volume expands and the density becomes relatively small. On the contrary, when the temperature drops, the volume of matter decreases and the density increases. But water is an exception, because the density of water is the highest at 4℃, and the density will decrease as long as the water temperature rises or falls from 4℃. That is to say, the volume of water at 4℃ is also expanding when it is heated and cooled. So water always freezes from the surface, and the water with the highest density of 4℃ will sink to the bottom. This attribute is very important. In the cold winter, although the water surface has been frozen, the lake bottom still maintains a temperature of about 4℃, so that the creatures in the water can safely spend the winter.

10. Density is an important characteristic of matter. According to the density, people can identify substances; Choosing substances with different densities can meet the different requirements of manufacturing; By measuring the density, other new substances may be found in scientific research.

1 1. The main unit of density in the international system of units is "kg/m3", which most students can master, but many students find it difficult to convert units. For example, the density of iron is 78× 103 kg/m3 = g/cm3. This problem can be solved by the basic method of unit conversion, that is, how many times the unit in the molecule becomes smaller, the converted value becomes larger:1kg =10 3g; How many times the unit in the denominator becomes smaller, the converted value becomes smaller: 1 m3 = 106 cm3, so according to this conversion method, 7.8×10kg/m3 = 7.8×103x (103/). The analysis shows that the unit of density has a law, that is, for the density of a certain substance, when "g/cm 3", "kg/DM 3" and "ton/m 3" are used as units, their values are the same. For example, the density of iron can be known according to this law: ρ water = 7.8g/cm 3 = 7.8kg/DM 3 = 7.8t/m 3. This "7.8" is obtained by subtracting 103 from the density value of iron in the density table in the textbook. Remembering this rule not only brings great convenience to the conversion of density units, but also makes some problems involving density calculation simple. For example, to calculate the mass of water, the mass of 1cm3 (ml) is 1g, the mass of 1cm3 (liter) is 1kg, and the mass of 1cm3 is1t.

[Edit this paragraph] The application of density

The application of density in production technology can be reflected in the following aspects.

1. can identify the materials that make up the object.

Density is one of the characteristics of matter. Every substance has a certain density, and the density of different substances is generally different. So we can use density to identify substances. The method is to measure the density of the measured substance, and compare the measured density with the density of various substances in the density table, so as to identify what substances the object is made of.

2. The composition of various substances contained in an object can be calculated.

3. It can calculate the mass of some objects that are difficult to weigh or the volume of objects with complex shapes.

According to the change of density formula: m=vρ or v=m/ρ, we can calculate the mass and volume of an object, especially some problems that are inconvenient to measure directly, such as calculating the volume of irregular objects and the mass of historic sites.

4. It can be judged whether the object is solid or hollow.

Use density knowledge to solve simple problems, such as judging whether an object is hollow or not, and use "analysis method" to solve some more complicated problems.

There are usually three ways to determine whether an object is hollow or solid:

(1) Calculate its density according to the formula, and then compare it with the density ρ of matter, if >: ρ, it is hollow; If = ρ, it is a solid.

(2) Given the mass, calculate V from the formula V = m/ρ, and then compare with V. If V >；; V is hollow; If V=V, it is a solid.

(3) treat the object as a solid object, use it to find the mass of a solid object with a volume of V, and then compare M with the actual mass of the object. If m >；; M, the object is hollow; If m=m, the object is solid.

5. The internal pressure and buoyancy of liquid can be calculated.

To sum up, visible density is widely used in scientific research, production and life. Density is an important basis for identifying unknown substances. Argon is discovered by calculating the density of an unknown gas. After many experiments and spectral analysis, it is confirmed that there is a new gas in the air, named argon. It can be used to judge soil fertility in agriculture. Soil rich in humus is fertile, and its density is generally 2.3× 103kg/m3. According to the density, the fertility of soil can be judged. When selecting seeds, seeds can be selected according to the ups and downs of seeds in water: full and strong seeds sink due to high density; The seeds of shriveled shells and other weeds float on the water because of their low density. In industrial production, such as the production of starch, potatoes are used as raw materials. Generally speaking, potatoes with more starch have higher density, so the yield of starch can be estimated by measuring the density of potatoes. For another example, before casting metal objects, the factory needs to estimate how much metal needs to be melted, and the required metal amount can be calculated according to the volume of the mold and the density of the metal.

[Edit this paragraph] Method of measuring object density

There are various methods to measure the density of objects, which can develop students' thinking. I summarized the following measurement methods:

[Edit this paragraph] I. Measuring solid density

Basic principle: ρ = m/v;

1, weighing method:

Equipment: balance, measuring cylinder, water, metal block and string.

Steps:

1. Weigh the mass of the metal block with a balance;

2. Inject a proper amount of water into the measuring cylinder, and the reading volume is V 1.

3. Tie the metal block with a string, put it into a measuring cylinder, immerse it in water, and read the volume as V2.

Calculation expression: ρ=m/(V2-V 1)

2, the specific gravity cup method:

Equipment: beaker, water, metal block, balance,

Steps:

1, fill the beaker with water and put it on the balance to weigh the mass as m1;

2. Gently put the metal block into the water to overflow some water, and then put the beaker on the balance to weigh the mass m2;

3. Take out the metal block, put the beaker on the balance and weigh the mass m3 of the beaker and the remaining water.

Calculation expression: ρ = ρ water (m2-m3)/(m 1-m3)

3, Archimedes principle law:

Equipment: spring scale, metal block, water, string.

Steps:

1, tie the metal block with a string, and weigh the gravity g of the metal block with a spring scale;

2. Immerse the metal block in water completely, and weigh the apparent weight of the metal block in water g/with a spring scale;

Calculation expression: ρ=Gρ water /(G-G)

4, buoyancy method (a):

Equipment: wood block, water, fine needle, measuring cylinder.

Steps:

1. Inject a proper amount of water into the measuring cylinder, and the reading volume is V1;

2. Put the wood block into the water, float and stand still, and read out the volume v2;

3. Insert the wood block with a fine needle, completely immerse the wood block in water, and read the volume as V3.

Calculation expression: ρ = ρ water (V2-V 1)/(V3-V 1)

5, buoyancy method (2):

Equipment: scale, cylindrical cup, water, small plastic cup, small stone.

Steps:

1. Put a proper amount of water in the cylindrical cup, then gently put the plastic cup mouth up and let it float, and measure the height of water in the cup with the scale h 1;

2. Gently put the pebbles into the cup, float, and measure the water height H2 with a scale;

3. Take the pebbles out of the cup, put them into the water, sink them into the water, and measure the height h3 of the water with a scale.

Calculation expression: ρ = ρ water (h2-h 1)/(h3-h 1)

6, densitometer method:

Equipment: eggs, densimeter, water, salt, glass.

Steps:

1, pour a proper amount of water into the glass, gently put the eggs in, and the eggs will sink;

2. gradually add salt to the water and stir with a densimeter while adding it until the eggs float. The density of brine measured by densimeter is equal to the density of eggs;

[Edit this paragraph] 2. Measuring liquid density

1, weighing method: