the main Natural science The relationship of mass and volume. Body density is the ratio of body weight to its volume

The relationship of mass and volume. Body density is the ratio of body weight to its volume

In the SI system, the density is measured in kg /, and in the GHS system in g /.

Specific gravity is the ratio of body weight to its volume

In the SI system, the specific gravity is measured in H / m 3, and in the GHS system in dyne / cm 3.

According to Newton’s second law, the weight is P \u003d mg, where g is the acceleration of gravity. Then the specific gravity can be represented as the product of the density of the body on the acceleration of gravity:

With a change in body temperature, its density also changes, as its volume changes. The dependence of body density on temperature is expressed by the formula:

where is the density of the body at 0 ° C, is the coefficient of volume expansion of the body, t is the temperature of the body.

There are several ways to determine the density of solids. If the body has the correct geometric shape, then its density is easy to determine by measuring its volume and mass. If the body has an irregular geometric shape, then its volume is determined using a beaker or the hydrostatic weighing method is used. To determine the volume of small and loose solids, as well as to determine the density of the liquid, a special device is used - a pycnometer.

In this laboratory work, the density of solids of regular geometric shape is determined, the volume of which is easy to calculate using the appropriate formulas.

The bodies of regular geometric shape in particular include: a ball for which volume:

where R is the radius, D is the diameter of the ball.

Cylinder for which volume:

; where D is the diameter of the cylinder, N is its height.

A hollow cylinder for which volume;

where D is the outer diameter of the cylinder, N is its height, d - the inner diameter of the cylinder.

The box for which the volume V \u003d a * b * cwhere but - height b -length,

with -parallelepiped width.

II. PERFORMANCE ORDER

1. Determine the body weight on the technical scales, while observing the rules for working with them. Pay attention to the accuracy of weighing on a technical balance.

2. Measure the linear dimensions of the body with a vernier caliper. Measure three times and calculate the average values.

3. Calculate the body volume from the average linear dimensions.

4. Measure the linear dimensions of the body with a micrometer (three times each size) and calculate the average body volume.

5. Calculate body density from average body mass and volume

separately for body measurements with vernier caliper and micrometer

7. Calculate the relative errors of measuring body density using the formula:

where m is the average value of body mass, is the average absolute error of measuring body mass, is the average relative error of measuring volume (formulas for calculating the relative errors of measuring body volume are given in the notes to this paper).

8. Calculate the absolute errors of density measurements using the formula (separately for micrometer and vernier caliper):

9. Enter the data of measurements and calculations in the tables.

10. Record the answers as: . separately for measuring body density with a caliper and micrometer.

12. Draw conclusions.

Table 1

Body volume

Tool name	No. rev.	Linear dimensions mm	Absolute errors, mm.	V	E%
BUT	at	with	Δa	Δв	Δc
	1.
2.
3.
Wed
	1.
2.
3.
Wed

Table 1 is for parallelepiped. For a cylinder, instead of a, b, c, there will be D. and H, etc.

table 2

Body density

Tool name	m, g	Δm, g

Formulas for calculating relative errors in measuring volume of bodies of regular geometric shape

For the ball:,

where D is the average diameter value, ΔD is the average absolute error of diameter measurements.

For cylinder: ,

where D and H are the average diameter and height, respectively, ΔD and ΔH are the average absolute errors of the diameter and height measurements of the cylinder.

For a hollow cylinder:

where D and d are the average values \u200b\u200bof the external and internal diameters, respectively, ΔD and Δd are the average values \u200b\u200bof the absolute errors of the measurements of the external and internal diameters, respectively, N is the average value of the height of the cylinder, and ΔH is the average value of the absolute errors of the height measurements.

For parallelepiped:

where a, b, c are average values \u200b\u200bof height, length and width, respectively, Δa, Δb, Δc are average values \u200b\u200bof absolute measurement errors.

test questions

1. What measurements are called direct and indirect? Give examples.

2. What errors are called systematic and random? What do they depend on?

3. What measurement errors are called absolute and relative? What is the dimension of these errors?

4. Give the concept of weight and body weight, density and specific gravity. What are the units of measurement for these quantities?

5. State the laws of Newton and the law of gravity.

6. Tell the caliper and micrometer device.

7. How does density depend on temperature?

LABORATORY WORK №2

STUDY OF LAWS OF VIBRATIONAL MOTION OF A MATHEMATICAL PENDULUM AND DETERMINATION OF ACCELERATION OF GRAVITY.

PURPOSE OF WORK: to study the laws of oscillatory motion, to determine the acceleration of gravity.

DEVICES AND ACCESSORIES: mathematical pendulum, stopwatch, set of balls, ruler.

1. SUMMARY OF THEORETICAL INFORMATION.

The movement in which the body or system of bodies at regular intervals deviates from the equilibrium position and returns to it again is called periodic oscillations.

Oscillations in which a change in an oscillating quantity with time occurs according to the law of sine or cosine are called harmonic.

The harmonic oscillation equation is written as:

Harmonic oscillations are characterized by the following parameters: amplitude A, period T, frequency υ, phase φ, circular frequency ω.

And - the amplitude of the oscillations - this is the largest offset from the equilibrium position. Amplitude is measured in units of length (m, cm, etc.).

T - period of oscillation - this is the time during which one complete oscillation takes place. The period is measured in seconds.

υ - Oscillation frequency is the number of oscillations per unit time. Measured in Hertz.

φ is the oscillation phase. The phase determines the position of the oscillating point at a given time. In the SI system, the phase is measured in radians.

ω - circular frequency is measured rad / s

Any oscillatory movement is performed under the action of a variable force. In the case of harmonic oscillation, this force is proportional to the displacement and directed against the displacement:

where K is the coefficient of proportionality, depending on body weight and circular frequency.

An example of harmonic oscillation is the oscillatory motion of a mathematical pendulum.

A mathematical pendulum is a material point suspended on a weightless and undeformable thread.

A small heavy ball suspended on a thin thread (inextensible) is a good model of a mathematical pendulum.

The volume of gases V is measured in cubic meters (m 3). Due to the fact that the volume of gases varies greatly during heating, cooling and compression, 1 m 3 of gas is taken as its unit under normal conditions (temperature - 0 ° C, pressure - 101.3 kPa). For these conditions, the basic characteristics of the gases are determined and thermal engineering calculations are performed. When accounting for gas consumption for commercial (financial) calculation, 1 m 3 is taken per unit volume under standard conditions (temperature - 20 ° C, pressure - 101.3 kPa, humidity - 0%).

The relationship between volume under normal and standard conditions:

V about \u003d V [(P b + p and) / 101.3] \u003d 2.695V (p abs / T); (2.7)

V 20 \u003d V 0 (273 + 20) / 273 \u003d 1,073 V 0, (2.8)

Where V is the volume of gas, m 3 measured under operating conditions; V 0 - the same, m 3, under normal conditions; V 20 is the same, m 3, at t \u003d 20 ° C and p \u003d 101.3 kPa.

Any gas can expand indefinitely. Therefore, knowledge of the volume occupied by the gas is not enough to determine its mass, since in any volume entirely filled with gas, its mass can be different.
Mass - a measure of the substance of a body (liquid, gas) at rest; scalar quantity characterizing the inertial and gravitational properties of the body. The unit of mass in SI is kilogram (kg).

Density, or mass per unit volume, denoted by the letter p, is the ratio of body weight m, kg, to its volume, V, m 3

P \u003d m / V (2.9)

Or taking into account the chemical formula of the gas:

P \u003d m / Vm \u003d M / 22.4, (2.10)

Where M is the molecular weight (see table. 2.3).

The unit of density in SI is kilogram per cubic meter (kg / m 3).

Knowing the composition of the gas mixture and the density of its components, we determine by the rule of mixing the average density of the mixture:

P cm \u003d (P 1 V 1 + P 2 V 2 + ... + P n V n) / 100, (2.11)

Where P 1, P 2 ... P n - the density of the components of the gas fuel, kg / m 3; V 1, V 2 ... V n - content of components, volume in%.
The reciprocal of the density is called the specific, or mass, volume V beats and is measured in cubic meters per kilogram (m 3 / kg).

In practice, often to show how much 1 m 3 of gas is lighter or heavier than 1 m 3 of air, they use the concept of "relative density d" - the ratio of gas density to air density:

D \u003d p / 1.293 or d \u003d M / (22.4x1.293) (2.12–2.13)

Table 2.3. The main characteristics of some gases that make up hydrocarbon gases and their combustion products.

Indicator	Nitrogen	Air	Water vapor	Carbon dioxide	Oxygen	Hydrogen	Carbon monoxide	Methane
Chemical formula	N 2	–	H 2 O	CO 2	O 2	H 2	CO	CH 4
Molecular Weight M	28,013	28,960	18,016	44,011	32,000	2,016	28,011	16,043
Molar volume VM, m 3 / kmol	22,395	22,398	22,405	22,262	22,393	22,425	22,400	22,38
The density of the gas phase, kg / m 3;
at 0 ° С and 101.3 kPa ρ P0	1,251	1,293	0,804	1,977	1,429	0,090	1,250	0,717
at 20 ° C and 101.3 kPa ρ P20	1,166	1,205	0,750	1,842	1,331	0,0837	1,165	0,668
The density of the liquid phase, kg / m 3 at 0 ° C and 101.3 kPa Jo	–	–	–	–	–	–	–	0,416
Relative gas density d n	0,9675	1,000	0,6219	1,529	1,105	0,0695	0,9667	0,5544
Specific gas constant R, J / (kg K)	296,65	281,53	452,57	185,26	259,7	4122,2	291,1	518,04
Temperature, ° С, at 101.3 kPa:
boiling t kin	-195,8	-195	100	-78,5	-183	-253	-192	-161
melting t pl	-210	-213	0	-56,5	-219	-259	-205	-182,5
Temperature is critical t crit ° C	-146,8	-139,2	374,3	31,84	-118,4	-240,2	-140	-82,5
Critical pressure p cr MPa	3,35	3,84	22,56	7,53	5,01	1,28	3,45	4,58
Heat of fusion Q plkJ / kg	25,62	–	–	190,26	13,86	173,40	33,60	255,80
Calorific value, MJ / m 3:
the highest Q in	–	–	–	–	–	12,80	12,68	39,93
inferior Q n	–	–	–	–	–	10,83	12,68	35,76
Calorific value, MJ / kg:
the highest Q in	–	–	–	–	–	141,90	10,09	55,56
inferior Q n	–	–	–	–	–	120,10	10,09	50,08
Wobbe number, MJ / m 3;
higher Wo b	–	–	–	–	–	48,49	12,90	53,30
inferior Wo h	–	–	–	–	–	41,03	12,9	48,23
Specific heat of gas with r, kJ / (kg ° С), at О ° С and:
constant pressure with p	1,042	1,008	1,865	0,819	0,920	14,238	1,042	2,171
constant volume with V	0,743	0,718	1,403	0,630	0,655	10,097	0,743	1,655
The specific heat of the liquid phase with w, kJ / (kg ° С), at 0 ° С and 101.3 kPa	–	–	–	–	–	–	–	3,461
Adiabatic exponent Χ, K, at 0 ° C and 101.3 kPa	1,401	1,404	1,330	1,310	1,404	1,410	1,401	1,320
Theoretically required amount of combustion air Lt.vm 3 / m 3	–	–	–	–	–	2,38	2,38	9,52
Theoretically required amount of oxygen for combustion L unnecessarilym 3 / m 3	–	–	–	–	–	0,5	0,5	2,0
The volume of wet combustion products, m 3 / m 3, with α \u003d 1;
CO 2	–	–	–	–	–	–	1,0	1,0
H 2 O	–	–	–	–	–	1,0	–	2,0
N 2	–	–	–	–	–	1,88	1,88	7,52
Total	–	–	–	–	–	2,88	2,88	10,52
Latent heat of vaporization at 101.3 kPa:
kJ / kg	–	–	–	–	–	–	–	512,4
kJ / l	–
Vapor volume with 1 kg of liquefied gases under normal conditions V p, m 3	–
Vapor volume with 1 liter of liquefied gases under normal conditions V p, m 3	–
Dynamic viscosity μ:
vapor phase, 107 N s / m 2	165,92	171,79	90,36	138,10	192,67	83,40	166,04	102,99
liquid phase, 106 N s / m 2	–							66,64
Kinematic viscosity ν, 106 m 2 / s	13,55	13,56	14,80	7,10	13,73	93,80	13,55	14,71
The solubility of gas in water, cm 3 / cm 3 at 0 ° C and 101.3 kPa	0,024	0,029	–	1,713	0,049	0,021	0,035	0,056
Flash point tBC, ° C	–					410–590	610–658	545–800
Heat output t° C	–					2210	2370	2045
Flammability limits of gases in a mixture with air at 0 ° С and 101.3 kPa, vol. %:
lower	–					4,0	12,5	5,0
upper	–					75,0	74,0	15,0
The content in the mixture, vol. %, with maximum flame propagation speed	–					38,5	45,0	9,8
Maximum flame speed vmax, m / s, in the pipe D \u003d 25.4 mm	–					4,83	1,25	0,67
The thermal conductivity of the components at 0 ° C and 101.3 kPa, W / (m K):
vaporous λ p	0,0243	0,0244	0,2373	0,0147	0,0247	0,1721	0,0233	0,0320
liquid λ w	–							0,306
The ratio of gas volume to liquid volume at a boiling point and pressure of 101.3 kPa	–							580
Octane number	–							110

Notes:
1. The Wobbe number is the ratio of the calorific value of gas to the square root of the relative density under standard conditions, which characterizes the constancy of the heat flow obtained by burning gas.
2. The adiabatic exponent is the ratio of the specific heat of a gas, respectively, at constant pressure and constant volume.
3. Viscosity (internal friction) is one of the phenomena of transport, the property of fluid bodies (liquids and gases) to resist the movement of one part relative to another. Distinguish between dynamic (units: Poise, Pa * s) and kinematic viscosity (units: Stokes, m 2 / s). Kinematic viscosity can be obtained as the ratio of dynamic viscosity to density of a substance.
4. Heat production - the maximum temperature that can be obtained with complete gas combustion in the theoretically necessary volume of dry air at a temperature of 0 ° C and no heat loss.

Homogeneous bodies can be made from solids. The homogeneity property is as follows. Let us select at random points on the body the parts that are the same in mass. The body is homogeneous if the volumes of these parts are the same. It is also possible to “make” bodies from liquids and gases by enclosing them in vessels.

For a homogeneous body, we can find out the dependence of mass on its volume. This dependence will be linear for any substances. However, for different substances, the angles of inclination of the corresponding graphs to the axis of volumes are different (Fig. 41). Therefore, we can conclude: the ratio of mass to volume for a given substance does not depend on volume, however, for different substances, these ratios are different. For example, the days of chart 3 (see Fig. 41), this ratio is larger than for chart 1.

The ratio is called the density of the substance. The density unit is kg / m 3.

Among metals, low densities are potassium, magnesium, lithium. The lightest metal - lithium - has a density of 534 kg / m 3 (this is less than the density of water). The metal with the highest density is osmium. Its density is 22 570 kg / m 3.

The density of a substance is related to its structure. This connection is manifested in the fact that the density is equal to the product of the concentration of particles and the mass of one particle (molecule, atom or ion) of the substance. Indeed, however, where is the total number of particles. So, .

Solid crystalline matter density may be related to the lattice period.

Let a substance (for example, copper) have a cubic face-centered lattice (Fig. 42). Then the volume contains 4 atoms. We determine the mass and volume of this cell.

If we take the mass of a substance equal to the molar mass, then it contains (Avogadro number) atoms. Therefore, the mass of the substance in the volume is equal. Thus, the density of copper is equal.

The density of gases varies easily, so it can change in different isoprocesses. This becomes clear if the Mendeleev-Clapeyron equation is written by including density in it. Indeed,; therefore, or. From this we can draw the following conclusions.

LABORATORY WORK №1

DETERMINATION OF DENSITY OF SOLID BODIES OF THE CORRECT GEOMETRIC FORM AND CALCULATION OF MEASUREMENT ERRORS

PURPOSE OF WORK: learn to use measuring instruments - a caliper, micrometer and technical scales, to master the method of approximate calculations, to acquire the necessary practical skills in processing experimental results, to determine the density of a solid body.

DEVICES AND ACCESSORIES: vernier caliper, micrometer, technical scales, weights, measured body.

1. SUMMARY OF THEORETICAL INFORMATION

Body density is the ratio of body weight to its volume