Russian Federation Protocol of the USSR State Standard

GSSSD 8-79 Liquid and gaseous air. Density, enthalpy, entropy and isobaric heat capacity at temperatures 70-1500 K and pressures 0.1-100 MPa

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STATE SERVICE OF STANDARD REFERENCE DATA

Standard reference data tables

AIR IS LIQUID AND GASED. DENSITY, ENTHALPY, ENTROPY AND ISOBARIC HEAT CAPACITY AT TEMPERATURES 70-1500 K AND PRESSURES 0.1-100 MPa

Tables of Standard Reference Data
Liquid and gaseous air Density, enthalpy, entropy and isobaric heat capacity at temperatures from 70 to 1500 K and pressures from 0.1 to 100 MPa

DEVELOPED by the All-Union Scientific Research Institute of Metrological Service, Odessa Institute of Engineers navy, Moscow Order of Lenin Energy Institute

RECOMMENDED FOR APPROVAL by the Soviet National Committee for the Collection and Evaluation of Numerical Data in the Field of Science and Technology of the Presidium of the USSR Academy of Sciences; All-Union Scientific Research Center Civil service standard reference data

APPROVED by the SSSSD expert commission consisting of:

Ph.D. tech. Sciences N.E. Gnezdilova, Doctor of Engineering. Sciences I.F. Golubeva, Doctor of Chemistry. Sciences L.V. Gurvich, Doctor of Engineering. Sciences B.A. Rabinovich, Doctor of Engineering. Sciences A.M. Sirota

PREPARED FOR APPROVAL by the All-Union Scientific Research Center of the State Service of Standard Reference Data

The use of standard reference data is mandatory in all sectors of the national economy

These tables contain the most important practical values ​​for the density, enthalpy, entropy and isobaric heat capacity of liquid and gaseous air.

The calculation of tables is based on the following principles:

1. The equation of state, which displays with high accuracy reliable experimental data on the , , -dependence, can provide a reliable calculation of caloric and acoustic properties using known thermodynamic relationships.

2. Averaging coefficients large number equations of state, equivalent in terms of accuracy of description of the initial information, allows us to obtain an equation that reflects the entire thermodynamic surface (for a selected set of experimental data among equations of the accepted type). Such averaging makes it possible to estimate the possible random error in the calculated values ​​of thermal, caloric and acoustic quantities, without taking into account the influence of the systematic error of experimental , , -data and the error caused by the choice of the form of the equation of state.

The averaged equation of state of liquid and gaseous air has the form

Where ; ; .

The equation is compiled based on the most reliable experimental density values ​​obtained in the works and covering the temperature range of 65-873 K and pressures of 0.01-228 MPa. The experimental data are described by an equation with a mean square error of 0.11%. The coefficients of the averaged equation of state were obtained as a result of processing a system of 53 equations that are equivalent in accuracy to the description of experimental data. In the calculations, the following values ​​of the gas constant and critical parameters were taken: 287.1 J/(kg K); 132.5 K; 0.00316 m/kg.

Coefficients of the average air state equation:

Enthalpy, entropy and isobaric heat capacity were determined using the formulas

Where , , are enthalpy, entropy and isochoric heat capacity in the ideal gas state. The values ​​of and are determined from the relations

Where and are enthalpy and entropy at temperature; - heat of sublimation at 0 K; - constant (0 in this work).

The value of the heat of sublimation of air was calculated based on data on the heat of sublimation of its components and is equal to 253.4 kJ/kg (in the calculations it was assumed that air does not contain CO and consists of 78.11% N, 20.96% O and 0.93% Ar by volume). The values ​​of enthalpy and entropy at a temperature of 100 K, which is an auxiliary reference point when integrating the equation for , are respectively 3.48115 kJ/kg and 20.0824 kJ/(kg K).

The isobaric heat capacity in the ideal gas state is borrowed from the work and approximated by a polynomial

The root mean square error of approximation of the initial data in the temperature range 50-2000 K is 0.009%, the maximum is about 0.02%.

Random errors of calculated values ​​are calculated with a confidence probability of 0.997 using the formula

Where is the average value of the thermodynamic function; - the value of the same function obtained by the th equation from a system containing equations.

Tables 1-4 show the values ​​of the thermodynamic functions of air, and Tables 5-8 show the corresponding random errors. The error values ​​in Tables 5-8 are presented for part of the isobars, and the values ​​for intermediate isobars can be obtained with acceptable accuracy by linear interpolation. Random errors in the calculated values ​​reflect the spread of the latter relative to the average equation of state; for density, they are significantly less than the mean square error in the description of the original array of experimental data, which serves as an integral estimate and includes large deviations for some data characterized by scatter.

Table 1

Air density

Continuation

	Kg/m, at , MPa,

table 2

Enthalpy of air

Continuation

	KJ/kg, at , MPa,

Table 3

Entropy of air

Continuation

	KJ/(kg, K), at , MPa,

Table 4

Isobaric heat capacity of air

________________

* The text of the document corresponds to the original. - Database manufacturer's note.

Continuation

	KJ/(kg, K), at , MPa,

Table 5. Mean square random errors of calculated density values

, %, at , MPa

Table 6. Root mean square random errors of calculated enthalpy values

KJ/kg, at , MPa

Due to the use of the virial form of the equation of state, the tables do not pretend to accurately describe the thermodynamic properties in the vicinity of the critical point (126-139 K, 190-440 kg/m).

Information about experimental studies of the thermodynamic properties of air, methods for compiling the equation of state and calculating tables, consistency of calculated values ​​with experimental data, as well as more detailed tables containing additional information about isochoric heat capacity, speed of sound, heat of evaporation, throttle effect, some derivatives and properties on boiling and condensation curves are given in the work.

BIBLIOGRAPHY

1. Nolborn L., Schultre N. die Druckwage und die Isothermen von Luft, Argon und Helium Zwischen 0 und 200 °C. - Ann. Phys. 1915 m, Bd 47, N 16, S.1089-1111.

2. Michels A., Wassenaar T., Van Seventer W. Isotherms of air between 0 °C and 75 °C and at pressures up to 2200 atm. -Appl. Sci. Res., 1953, vol. 4, No. 1, p.52-56.

3. Compressibility isotherms of air at temperatures between -25 °C and -155 °C and at densities up to 560 Amagats (Pressures up to 1000 atmospheres) / Michels A.. Wassenaar T., Levelt J.M., De Graaff W. - Appl . Sci. Res., 1954, vol. A 4, N 5-6, p.381-392.

4. Experimental study specific volumes of air/Vukalovich M.P., Zubarev V.N., Aleksandrov A.A., Kozlov A.D. - Thermal power engineering, 1968, N 1, p. 70-73.

5. Romberg N. Neue Messungen der thermischen ler Luft bei tiefen Temperaturen and die Berechnung der kalorischen mit Hilfe des Kihara-Potentials. - VDl-Vorschungsheft, 1971, - N 543, S.1-35.

6. Blanke W. Messung der thermischen von Luft im Zweiphasengebiet und Seiner Umgebung. Dissertation zur Erlangung des Grades eines Doctor-Ingenieurs/. Bohum., 1973.

7. Measurement of air density at temperatures 78-190 K up to a pressure of 600 bar / Wasserman A.A., Golovsky E.A., Mitsevich E.P., Tsymarny V.A., M., 1975. (Deposited in VINITI 28.07 .76 N 2953-76).

8. Landolt N., R. Zahlenwerte und Funktionen aus Physik, Chemie, Astronomic, Geophysik und Technik. Berlin., Springer Verlag, 1961, Bd.2.

9. Tables of thermal properties of gases. Wachington, Gov. print, off., 1955, XI. (U.S. Dep. of commerce. NBS. Girc. 564).

10. Thermodynamic properties of air/Sychev V.V., Wasserman A.A., Kozlov A.D. and others. M., Standards Publishing House, 1978.

Laboratory work No. 1

Definition of mass isobar

heat capacity of air

Heat capacity is the heat that must be added to a unit amount of a substance to heat it by 1 K. A unit amount of a substance can be measured in kilograms, cubic meters under normal physical conditions, and kilomoles. A kilomole of gas is the mass of a gas in kilograms, numerically equal to its molecular weight. Thus, there are three types of heat capacities: mass c, J/(kg⋅K); volumetric s′, J/(m3⋅K) and molar, J/(kmol⋅K). Since a kilomole of gas has a mass μ times greater than one kilogram, a separate designation for molar heat capacity is not introduced. Relationships between heat capacities:

where = 22.4 m3/kmol is the volume of a kilomol of an ideal gas under normal physical conditions; – gas density under normal physical conditions, kg/m3.

The true heat capacity of a gas is the derivative of heat with respect to temperature:

The heat supplied to the gas depends on the thermodynamic process. It can be determined by the first law of thermodynamics for isochoric and isobaric processes:

Here is the heat supplied to 1 kg of gas in an isobaric process; - change internal energy gas; – work of gases against external forces.

Essentially, formula (4) formulates the 1st law of thermodynamics, from which Mayer’s equation follows:

If we put = 1 K, then , that is physical meaning gas constant is the work done by 1 kg of gas in an isobaric process when its temperature changes by 1 K.

Mayer's equation for 1 kilomole of gas has the form

where = 8314 J/(kmol⋅K) is the universal gas constant.

In addition to the Mayer equation, the isobaric and isochoric mass heat capacities of gases are related to each other through the adiabatic exponent k (Table 1):

Table 1.1

Values ​​of adiabatic exponents for ideal gases

Atomicity of gases
Monatomic gases
Diatomic gases
Tri- and polyatomic gases

GOAL OF THE WORK

Consolidation of theoretical knowledge on the basic laws of thermodynamics. Practical development of the method for determining the heat capacity of air based on the energy balance.

Experimental determination of the specific mass heat capacity of air and comparison of the obtained result with the reference value.

1.1. Description of the laboratory setup

The installation (Fig. 1.1) consists of a brass pipe 1 with internal diameter d =
= 0.022 m, at the end of which there is an electric heater with thermal insulation 10. An air flow moves inside the pipe, which is supplied 3. The air flow can be regulated by changing the fan speed. Pipe 1 contains a full pressure tube 4 and excess static pressure 5, which are connected to pressure gauges 6 and 7. In addition, a thermocouple 8 is installed in pipe 1, which can move along the cross section simultaneously with the full pressure tube. The magnitude of the emf of the thermocouple is determined by potentiometer 9. Heating of the air moving through the pipe is regulated using a laboratory autotransformer 12 by changing the power of the heater, which is determined by the readings of ammeter 14 and voltmeter 13. The temperature of the air at the outlet of the heater is determined by thermometer 15.

1.2. EXPERIMENTAL PROCEDURE

Heat flow of the heater, W:

where I – current, A; U – voltage, V; = 0.96; =
= 0.94 – heat loss coefficient.

Fig.1.1. Experimental setup diagram:

1 – pipe; 2 – confuser; 3 – fan; 4 – tube for measuring dynamic pressure;

5 – pipe; 6, 7 – differential pressure gauges; 8 – thermocouple; 9 – potentiometer; 10 – insulation;

11 – electric heater; 12 – laboratory autotransformer; 13 – voltmeter;

14 – ammeter; 15 – thermometer

Heat flux absorbed by air, W:

where m – mass air flow, kg/s; – experimental, mass isobaric heat capacity of air, J/(kg K); – air temperature at the exit from the heating section and at the entrance to it, °C.

Mass air flow, kg/s:

. (1.10)

Here is the average air speed in the pipe, m/s; d – internal diameter of the pipe, m; – air density at temperature, which is found by the formula, kg/m3:

, (1.11)

where = 1.293 kg/m3 – air density under normal physical conditions; B – pressure, mm. rt. st; – excess static air pressure in the pipe, mm. water Art.

Air velocities are determined by dynamic pressure in four equal sections, m/s:

where is the dynamic pressure, mm. water Art. (kgf/m2); g = 9.81 m/s2 – acceleration free fall.

Average air speed in the pipe cross-section, m/s:

The average isobaric mass heat capacity of air is determined from formula (1.9), into which the heat flow is substituted from equation (1.8). The exact value of the heat capacity of air at average air temperature is found from the table of average heat capacities or from the empirical formula, J/(kg⋅K):

. (1.14)

Relative error of experiment, %:

. (1.15)

1.3. Conducting the experiment and processing

measurement results

The experiment is carried out in the following sequence.

1. The laboratory stand is turned on and after establishing a stationary mode, the following readings are taken:

Dynamic air pressure at four points of equal pipe sections;

Excessive static air pressure in the pipe;

Current I, A and voltage U, V;

Inlet air temperature, °C (thermocouple 8);

Outlet temperature, °C (thermometer 15);

Barometric pressure B, mm. rt. Art.

The experiment is repeated for the next mode. The measurement results are entered in Table 1.2. Calculations are performed in table. 1.3.

Table 1.2

Measurement table

	Name of quantity
	Air inlet temperature, °C
	Outlet air temperature, °C
	Dynamic air pressure, mm. water Art.
	Excessive static air pressure, mm. water Art.
	Barometric pressure B, mm. rt. Art.
	Voltage U, V

Table 1.3

Calculation table

	Name of quantities
	Dynamic pressure, N/m2
	Average inlet flow temperature, °C

TEMPERATURE. It is measured in both Kelvin (K) and degrees Celsius (°C). The Celsius size and the Kelvin size are the same for temperature differences. Relationship between temperatures:

t = T - 273.15 K,

Where t— temperature, °C, T— temperature, K.

PRESSURE. Humid air pressure p and its components are measured in Pa (Pascal) and multiple units (kPa, GPa, MPa).
Barometric pressure of humid air p b equal to the sum of the partial pressures of dry air p in and water vapor p p :

p b = p c + p p

DENSITY. Density of humid air ρ , kg/m3, is the ratio of the mass of the air-steam mixture to the volume of this mixture:

ρ = M/V = M in /V + M p /V

The density of moist air can be determined by the formula

ρ = 3.488 p b /T - 1.32 p p /T

SPECIFIC GRAVITY. Specific gravity of moist air γ - this is the ratio of the weight of moist air to the volume it occupies, N/m 3. Density and specific gravity are related by the relationship

ρ = γ /g,

Where g— free fall acceleration equal to 9.81 m/s 2 .

AIR HUMIDITY. Water vapor content in the air. characterized by two quantities: absolute and relative humidity.
Absolute air humidity. the amount of water vapor, kg or g, contained in 1 m 3 of air.
Relative air humidity φ , expressed in %. the ratio of the partial pressure of water vapor contained in the air to the partial pressure of water vapor in the air when it is completely saturated with water vapor p.p. :

φ = (p p /p bp) 100%

The partial pressure of water vapor in saturated humid air can be determined from the expression

lg p p.n. = 2.125 + (156 + 8.12t h.n.)/(236 + t h.n.),

Where t v.n.— temperature of saturated humid air, °C.

DEW POINT. The temperature at which the partial pressure of water vapor p p contained in moist air is equal to the partial pressure of saturated water vapor p p.n. at the same temperature. At dew temperature, moisture begins to condense from the air.

d = M p / M in

d = 622p p / (p b - p p) = 6.22φp bp (p b - φp bp /100)

SPECIFIC HEAT. Specific heat capacity of moist air c, kJ/(kg * °C) is the amount of heat required to heat 1 kg of a mixture of dry air and water vapor by 10 and referred to 1 kg of dry air:

c = c c + c p d /1000,

Where c in- average specific heat capacity of dry air, taken in the temperature range 0-1000C equal to 1.005 kJ/(kg * °C); c p is the average specific heat capacity of water vapor, equal to 1.8 kJ/(kg * °C). For practical calculations when designing heating, ventilation and air conditioning systems, it is allowed to use the specific heat capacity of moist air c = 1.0056 kJ/(kg * °C) (at a temperature of 0°C and a barometric pressure of 1013.3 GPa)

SPECIFIC ENTHALPY. The specific enthalpy of moist air is the enthalpy I, kJ, referred to 1 kg of dry air mass:

I = 1.005t + (2500 + 1.8068t) d / 1000,
or I = ct + 2.5d

VOLUMETRIC EXPANSION COEFFICIENT. Temperature coefficient of volumetric expansion

α = 0.00367 °C -1
or α = 1/273 °C -1.

MIXTURE PARAMETERS .
Air mixture temperature

t cm = (M 1 t 1 + M 2 t 2) / (M 1 + M 2)

d cm = (M 1 d 1 + M 2 d 2) / (M 1 + M 2)

Specific enthalpy of air mixture

I cm = (M 1 I 1 + M 2 I 2) / (M 1 + M 2)

Where M1, M2- mass of mixed air

FILTERS CLASSES

Application	Cleaning class					Degree of purification
	Standards	DIN 24185 DIN 24184	EN 779	EUROVENT 4/5	EN 1882
Filter for coarse cleaning with low requirements for air purity	Rough cleaning	EU1	G1	EU1	—	A%
A filter used for high concentrations of dust with rough cleaning, air conditioning and exhaust ventilation with low requirements for indoor air purity.						65
		EU2	G2	EU2	—	80
		EU3	G3	EU3	—	90
		EU4	G4	EU4	—
Separation of fine dust in ventilation equipment used in rooms with high air quality requirements. Filter for very fine filtration. The second stage of purification (additional purification) in rooms with average requirements for air purity.	Fine cleaning	EU5	EU5	EU5	—	E%
						60
		EU6	EU6	EU6	—	80
		EU7	EU7	EU7	—	90
		EU8	EU8	EU8	—	95
		EU9	EU9	EU9	—
Cleaning from ultrafine dust. It is used in rooms with increased requirements for air purity ("clean room"). Final air purification in rooms with precision equipment, surgical units, intensive care wards, and in the pharmaceutical industry.	Extra fine cleaning	—	—	—	EU5	WITH%
						97
		—	—	—	EU6	99
		—	—	—	EU7	99,99
		—	—	—	EU8	99,999

CALCULATION OF HEATING POWER

Heating, °C
m 3 / h	5	10	15	20	25	30	35	40	45	50
100	0.2	0.3	0.5	0.7	0.8	1.0	1.2	1.4	1.5	1.7
200	0.3	0.7	1.0	1.4	1.7	2.0	2.4	2.7	3.0	3.4
300	0.5	1.0	1.5	2.0	2.5	3.0	3.6	4.1	4.6	5.1
400	0.7	1.4	2.0	2.7	3.4	4.1	4.7	5.4	6.1	6.8
500	0.8	1.7	2.5	3.4	4.2	5.1	5.9	6.8	7.6	8.5
600	1.0	2.0	3.0	4.1	5.1	6.1	7.1	8.1	9.1	10.1
700	1.2	2.4	3.6	4.7	5.9	7.1	8.3	9.5	10.7	11.8
800	1.4	2.7	4.1	5.4	6.8	8.1	9.5	10.8	12.2	13.5
900	1.5	3.0	4.6	6.1	7.6	9.1	10.7	12.2	13.7	15.2
1000	1.7	3.4	5.1	6.8	8.5	10.1	11.8	13.5	15.2	16.9
1100	1.9	3.7	5.6	7.4	9.3	11.2	13.0	14.9	16.7	18.6
1200	2.0	4.1	6.1	8.1	10.1	12.2	14.2	16.2	18.3	20.3
1300	2.2	4.4	6.6	8.8	11.0	13.2	15.4	17.6	19.8	22.0
1400	2.4	4.7	7.1	9.5	11.8	14.2	16.6	18.9	21.3	23.7
1500	2.5	5.1	7.6	10.1	12.7	15.2	17.8	20.3	22.8	25.4
1600	2.7	5.4	8.1	10.8	13.5	16.2	18.9	21.6	24.3	27.1
1700	2.9	5.7	8.6	11.5	14.4	17.2	20.1	23.0	25.9	28.7
1800	3.0	6.1	9.1	12.2	15.2	18.3	21.3	24.3	27.4	30.4
1900	3.2	6.4	9.6	12.8	16.1	19.3	22.5	25.7	28.9	32.1
2000	3.4	6.8	10.1	13.5	16.9	20.3	23.7	27.1	30.4	33.8

STANDARDS AND REGULATIONS

SNiP 2.01.01-82 – Construction climatology and geophysics

Information about climatic conditions specific territories.

SNiP 2.04.05-91* - Heating, ventilation and air conditioning

Real building codes should be observed when designing heating, ventilation and air conditioning in the premises of buildings and structures (hereinafter referred to as buildings). When designing, you should also comply with the heating, ventilation and air conditioning requirements of SNiP of the relevant buildings and premises, as well as departmental standards and other regulatory documents approved and agreed upon by the State Construction Committee of Russia.

SNiP 2.01.02-85* - Fire safety standards

These standards must be observed when developing projects for buildings and structures.

These standards establish fire-technical classification of buildings and structures, their elements, building structures, materials, as well as general fire safety requirements for structural and planning solutions for premises, buildings and structures for various purposes.

These standards are supplemented and clarified by the fire safety requirements set out in SNiP Part 2 and in other regulatory documents approved or agreed upon by the State Construction Committee.

SNiP II-3-79* - Construction heating engineering

These building heating engineering standards must be observed when designing enclosing structures (external and internal walls, partitions, coverings, attic and interfloor ceilings, floors, filling openings: windows, lanterns, doors, gates) of new and reconstructed buildings and structures for various purposes (residential, public , production and auxiliary industrial enterprises, agricultural and warehouse, with standardized temperature or temperature and relative humidity of internal air).

SNiP II-12-77 - Noise protection

These standards and rules must be observed when designing noise protection to ensure acceptable sound pressure levels and sound levels in workplaces in industrial and auxiliary buildings and on the sites of industrial enterprises, in residential and public buildings, as well as in residential areas of cities and towns. other settlements.

SNiP 2.08.01-89* - Residential buildings

These norms and rules apply to the design of residential buildings (apartment buildings, including apartment buildings for the elderly and families with disabled people using wheelchairs, hereinafter referred to as families with disabled people, as well as dormitories) with a height of up to 25 floors inclusive.

These rules and regulations do not apply to the design of inventory and mobile buildings.

SNiP 2.08.02-89* - Public buildings and structures

These rules and regulations apply to the design of public buildings (up to 16 floors inclusive) and structures, as well as public premises built into residential buildings. When designing public premises built into residential buildings, you should additionally be guided by SNiP 2.08.01-89* (Residential buildings).

SNiP 2.09.04-87* - Administrative and domestic buildings

These standards apply to the design of administrative and residential buildings up to 16 floors inclusive and enterprise premises. These standards do not apply to the design of administrative buildings and public premises.

When designing buildings being rebuilt in connection with the expansion, reconstruction or technical re-equipment of enterprises, deviations from these standards in terms of geometric parameters are allowed.

SNiP 2.09.02-85* - Industrial buildings

These standards apply to the design of industrial buildings and premises. These standards do not apply to the design of buildings and premises for the production and storage of explosives and blasting means, underground and mobile (inventory) buildings.

SNiP 111-28-75 - Rules for production and acceptance of work

Start-up tests of installed ventilation and air conditioning systems are carried out in accordance with the requirements of SNiP 111-28-75 "Rules for production and acceptance of work" after mechanical testing of ventilation and related power equipment. The purpose of commissioning tests and adjustment of ventilation and air conditioning systems is to establish compliance of their operating parameters with design and standard indicators.

Before testing begins, ventilation and air conditioning units must operate continuously and properly for 7 hours.

During startup tests the following must be carried out:

• Checking the compliance of the parameters of the installed equipment and elements of ventilation devices adopted in the project, as well as the compliance of the quality of their manufacture and installation with the requirements of TU and SNiP.
• Detecting leaks in air ducts and other system elements
• Checking compliance with the design data of volumetric air flow rates passing through air intake and air distribution devices of general ventilation and air conditioning installations
• Checking compliance with the passport data of ventilation equipment for performance and pressure
• Checking the uniform heating of heaters. (If there is no coolant during the warm period of the year, the uniform heating of the heaters is not checked)

TABLE OF PHYSICAL QUANTITIES

Fundamental Constants
Avogadro's constant (number)	N A	6.0221367(36)*10 23 mol -1
Universal gas constant	R	8.314510(70) J/(mol*K)
Boltzmann's constant	k=R/NA	1.380658(12)*10 -23 J/K
Absolute zero temperature	0K	-273.150C
Speed ​​of sound in air under normal conditions		331.4 m/s
Gravity acceleration	g	9.80665 m/s 2
Length (m)
micron	μ(μm)	1 µm = 10 -6 m = 10 -3 cm
angstrom	-	1 - = 0.1 nm = 10 -10 m
yard	yd	0.9144 m = 91.44 cm
foot	ft	0.3048 m = 30.48 cm
inch	in	0.0254 m = 2.54 cm
Area, m2)
square yard	yd 2	0.8361 m2
square foot	ft 2	0.0929 m2
square inch	in 2	6.4516 cm 2
Volume, m3)
cubic yard	yd 3	0.7645 m 3
cubic foot	ft 3	28.3168 dm 3
cubic inch	in 3	16.3871 cm 3
gallon (English)	gal (UK)	4.5461 dm 3
gallon (US)	gal (US)	3.7854 dm 3
pint (English)	pt (UK)	0.5683 dm 3
dry pint (USA)	dry pt (US)	0.5506 dm 3
liquid pint (US)	liq pt (US)	0.4732 dm 3
fluid ounce (English)	fl.oz (UK)	29.5737 cm 3
fluid ounce (US)	fl.oz (US)	29.5737 cm 3
bushel (US)	bu (US)	35.2393 dm 3
dry barrel (USA)	bbl (US)	115.628 dm 3
Weight (kg)
lb.	lb	0.4536 kg
slug	slug	14.5939 kg
gran	gr	64.7989 mg
trade ounce	oz	28.3495 g
Density (kg/m3)
pound per cubic foot	lb/ft 3	16.0185 kg/m 3
pound per cubic inch	lb/in 3	27680 kg/m 3
slug per cubic foot	slug/ft 3	515.4 kg/m 3
Thermodynamic temperature (K)
degree Rankine	°R	5/9 K
Temperature (K)
degrees Fahrenheit	°F	5/9 K; t°C = 5/9*(t°F - 32)
Force, weight (N or kg*m/s 2)
newton	N	1 kg*m/s 2
poundal	pdl	0.1383 H
lbf	lbf	4.4482 H
kilogram-force	kgf	9.807 H
Specific Gravity (N/m3)
lbf per cubic inch	lbf/ft 3	157.087 N/m 3
Pressure (Pa or kg/(m*s 2) or N/m 2)
pascal	Pa	1 N/m 2
hectopascal	GPa	10 2 Pa
kilopascal	kPa	10 3 Pa
bar	bar	10 5 N/m 2
the atmosphere is physical	atm	1.013*10 5 N/m 2
millimeter of mercury	mm Hg	1.333*10 2 N/m 2
kilogram-force per cubic centimeter	kgf/cm 3	9.807*10 4 N/m 2
pound per square foot	pdl/ft 2	1.4882 N/m 2
lbf per square foot	lbf/ft 2	47.8803 N/m 2
lbf per square inch	lbf/in 2	6894.76 N/m 2
foot of water	ftH2O	2989.07 N/m 2
inch of water	inH2O	249.089 N/m 2
inch of mercury	in Hg	3386.39 N/m 2
Work, energy, heat (J or kg * m 2 / s 2 or N * m)
joule	J	1 kg*m 2 /s 2 = 1 N*m
calorie	cal	4.187 J
kilocalorie	Kcal	4187 J
kilowatt-hour	kwh	3.6*10 6 J
British thermal unit	Btu	1055.06 J
foot-pound	ft*pdl	0.0421 J
ft-lbf	ft*lbf	1.3558 J
liter-atmosphere	l*atm	101.328 J
Power, W)
foot pound per second	ft*pdl/s	0.0421 W
ft-lbf per second	ft*lbf/s	1.3558 W
horsepower (English)	hp	745.7 W
British thermal unit per hour	Btu/h	0.2931 W
kilogram-force meter per second	kgf*m/s	9.807 W
Mass flow (kg/s)
pound-mass per second	lbm/s	0.4536 kg/s
Thermal conductivity coefficient (W/(m*K))
British thermal unit per second foot-degree Fahrenheit	Btu/(s*ft*degF)	6230.64 W/(m*K)
Heat transfer coefficient (W/(m 2 *K))
British thermal unit per second - square foot degrees Fahrenheit	Btu/(s*ft 2 *degF)	20441.7 W/(m 2 *K)
Thermal diffusivity coefficient, kinematic viscosity (m 2 /s)
Stokes	St	10 -4 m 2 /s
centistokes	cSt (cSt)	10 -6 m 2 /s = 1mm 2 /s
square foot per second	ft 2 /s	0.0929 m 2 /s
Dynamic viscosity (Pa*s)
poise	P (P)	0.1 Pa*s
centipoise cP	(sp)	10 6 Pa*s
poundal second per square foot	pdt*s/ft 2	1.488 Pa*s
pound-force second per square foot	lbf*s/ft 2	47.88 Pa*s
Specific heat capacity (J/(kg*K))
calorie per gram degree Celsius	cal/(g*°C)	4.1868*10 3 J/(kg*K)
British thermal unit per pound degree Fahrenheit	Btu/(lb*degF)	4187 J/(kg*K)
Specific entropy (J/(kg*K))
British thermal unit per pound degree Rankine	Btu/(lb*degR)	4187 J/(kg*K)
Heat flux density (W/m2)
kilocalorie per square meter - hour	Kcal/(m 2 *h)	1.163 W/m2
British thermal unit per square foot - hour	Btu/(ft 2 *h)	3.157 W/m2
Moisture permeability of building structures
kilogram per hour per meter millimeter of water column	kg/(h*m*mm H 2 O)	28.3255 mg(s*m*Pa)
Volumetric permeability of building structures
cubic meter per hour per meter-millimeter water column	m 3 /(h*m*mm H 2 O)	28.3255*10 -6 m 2 /(s*Pa)
The power of light
candela	cd	SI base unit
Illumination (lx)
luxury	OK	1 cd*sr/m 2 (sr - steradian)
ph	ph (ph)	10 4 lx
Brightness (cd/m2)
stilb	st (st)	10 4 cd/m 2
nit	nt (nt)	1 cd/m2

INROST Group of Companies

Under specific heat capacity substances understand the amount of heat that must be added or subtracted from a unit of substance (1 kg, 1 m 3, 1 mol) in order to change its temperature by one degree.

Depending on the unit of a given substance, the following specific heat capacities are distinguished:

Mass heat capacity WITH, referred to 1 kg of gas, J/(kg∙K);

Molar heat capacity µС, referred to 1 kmol of gas, J/(kmol∙K);

Volumetric heat capacity WITH', referred to 1 m 3 of gas, J/(m 3 ∙K).

Specific heat capacities are related to each other by the relation:

Where υ n- specific volume of gas under normal conditions (n.s.), m 3 /kg; µ - molar mass gas, kg/kmol.

The heat capacity of an ideal gas depends on the nature of the process of supplying (or removing) heat, on the atomicity of the gas and temperature (the heat capacity of real gases also depends on pressure).

Relationship between mass isobaric With P and isochoric C V heat capacities are established by the Mayer equation:

C P - C V = R, (1.2)

Where R – gas constant, J/(kg∙K).

When an ideal gas is heated in a closed vessel of constant volume, heat is spent only on changing the energy of motion of its molecules, and when heated at constant pressure, due to the expansion of the gas, work is simultaneously performed against external forces.

For molar heat capacities, Mayer's equation has the form:

µС р - µС v = µR, (1.3)

Where µR=8314J/(kmol∙K) – universal gas constant.

Ideal gas volume V n, reduced to normal conditions, is determined from the following relation:

(1.4)

Where R n– pressure under normal conditions, R n= 101325 Pa = 760 mmHg; Tn– temperature under normal conditions, Tn= 273.15 K; P t, Vt, T t– operating pressure, volume and temperature of the gas.

The ratio of isobaric to isochoric heat capacity is denoted by k and call adiabatic index:

(1.5)

From (1.2) and taking into account (1.5) we obtain:

For accurate calculations, the average heat capacity is determined by the formula:

(1.7)

In thermal calculations of various equipment, the amount of heat required to heat or cool gases is often determined:

Q = C∙m∙(t 2 - t 1), (1.8)

Q = C′∙V n∙(t 2 - t 1), (1.9)

Where V n– volume of gas at standard conditions, m3.

Q = µC∙ν∙(t 2 - t 1), (1.10)

Where ν – amount of gas, kmol.

Heat capacity. Using heat capacity to describe processes in closed systems

In accordance with equation (4.56), heat can be determined if the change in entropy S of the system is known. However, the fact that entropy cannot be measured directly creates some complications, especially when describing isochoric and isobaric processes. There is a need to determine the amount of heat using a quantity measured experimentally.

This value can be the heat capacity of the system. Most general definition heat capacity follows from the expression of the first law of thermodynamics (5.2), (5.3). Based on it, any capacity of the system C with respect to work of type m is determined by the equation

C m = dA m / dP m = P m d e g m / dP m , (5.42)

where C m is the system capacity;

P m and g m are, respectively, the generalized potential and state coordinate of type m.

The value C m shows how much work of type m must be done under given conditions in order to change the mth generalized potential of the system by its unit of measurement.

The concept of the capacity of a system in relation to a particular work in thermodynamics is widely used only when describing the thermal interaction between the system and the environment.

The capacity of the system in relation to heat is called heat capacity and is given by the equality

C = d e Q / dT = Td e S heat / dT. (5.43)

Thus, Heat capacity can be defined as the amount of heat that must be imparted to a system to change its temperature by one Kelvin.

Heat capacity, like internal energy and enthalpy, is an extensive quantity proportional to the amount of matter. In practice, the heat capacity per unit mass of a substance is used - specific heat capacity, and the heat capacity per one mole of the substance, – molar heat capacity. Specific heat capacity in SI is expressed in J/(kg K), and molar capacity in J/(mol K).

Specific and molar heat capacities are related by the relation:

C mol = C beat M, (5.44)

where M - molecular mass substances.

Distinguish true (differential) heat capacity, determined from equation (5.43) and representing the elementary increment of heat with an infinitesimal change in temperature, and average heat capacity, which is the ratio of the total amount of heat to the total change in temperature in this process:

Q/DT. (5.45)

The relationship between true and average specific heat capacity is established by the relation

At constant pressure or volume, heat and, accordingly, heat capacity acquire the properties of a state function, i.e. become characteristics of the system. It is these heat capacities - isobaric C P (at constant pressure) and isochoric C V (at constant volume) that are most widely used in thermodynamics.

If the system is heated at a constant volume, then, in accordance with expression (5.27), the isochoric heat capacity C V is written in the form

C V = . (5.48)

If the system is heated at constant pressure, then, in accordance with equation (5.32), the isobaric heat capacity С Р appears in the form

C P = . (5.49)

To find the connection between С Р and С V, it is necessary to differentiate expression (5.31) with respect to temperature. For one mole of an ideal gas, this expression, taking into account equation (5.18), can be represented as

H = U + pV = U + RT. (5.50)

dH/dT = dU/dT + R, (5.51)

and the difference between the isobaric and isochoric heat capacities for one mole of an ideal gas is numerically equal to the universal gas constant R:

C R - C V = R . (5.52)

The heat capacity at constant pressure is always greater than the heat capacity at constant volume, since heating a substance at constant pressure is accompanied by the work of gas expansion.

Using the expression for the internal energy of an ideal monatomic gas (5.21), we obtain the value of its heat capacity for one mole of an ideal monatomic gas:

C V = dU/dT = d(3/2 RT)dT = 3/2 R » 12.5 J/(mol K); (5.53)

C P = 3/2R + R = 5/2 R » 20.8 J/(mol K). (5.54)

Thus, for monatomic ideal gases, C V and C p do not depend on temperature, since all the supplied thermal energy is spent only on accelerating translational motion. For polyatomic molecules, along with a change in translational motion, a change in rotational and vibrational intramolecular motion can also occur. For diatomic molecules, additional rotational motion is usually taken into account, as a result of which the numerical values ​​of their heat capacities are:

C V = 5/2 R » 20.8 J/(mol K); (5.55)

C p = 5/2 R + R = 7/2 R » 29.1 J/(mol K). (5.56)

Along the way, let’s touch on the heat capacities of substances in other substances (except gaseous) states of aggregation. To estimate the heat capacities of solid chemical compounds, the approximate Neumann and Kopp additivity rule is often used, according to which the molar heat capacity of chemical compounds in the solid state is equal to the sum of the atomic heat capacities of the elements included in a given compound. Thus, the heat capacity of a complex chemical compound Taking into account the Dulong and Petit rule, it can be estimated as follows:

C V = 25n J/(mol K), (5.57)

where n is the number of atoms in the molecules of the compounds.

The heat capacities of liquids and solids near the melting point (crystallization) are almost equal. Near the normal boiling point, most organic liquids have a specific heat capacity of 1700 - 2100 J/kg K. In the intervals between these phase transition temperatures, the heat capacity of the liquid can differ significantly (depending on temperature). IN general view The dependence of the heat capacity of solids on temperature in the range 0 – 290K in most cases is well conveyed by the semi-empirical Debye equation (for a crystal lattice) in the low temperature region

C P » C V = eT 3, (5.58)

in which the proportionality coefficient (e) depends on the nature of the substance (empirical constant).

The dependence of the heat capacity of gases, liquids and solids on temperature at ordinary and high temperatures is usually expressed using empirical equations in the form of power series:

C P = a + bT + cT 2 (5.59)

C P = a + bT + c"T -2, (5.60)

where a, b, c and c" are empirical temperature coefficients.

Returning to the description of processes in closed systems using the heat capacity method, let us write some of the equations given in paragraph 5.1 in a slightly different form.

Isochoric process. Expressing internal energy (5.27) in terms of heat capacity, we obtain

dU V = dQ V = U 2 – U 1 = C V dT = C V dT . (5.61)

Taking into account the fact that the heat capacity of an ideal gas does not depend on temperature, equation (5.61) can be written as follows:

DU V = Q V = U 2 - U 1 = C V DT . (5.62)

To calculate the value of the integral (5.61) for real mono- and polyatomic gases, you need to know the specific form of the functional dependence C V = f(T) type (5.59) or (5.60).

Isobaric process. For the gaseous state of a substance, the first law of thermodynamics (5.29) for this process, taking into account the work of expansion (5.35) and using the heat capacity method, is written as follows:

Q P = C V DT + RDT = C P DT = DH (5.63)

Q Р = DH Р = H 2 – H 1 = C Р dT. (5.64)

If the system is an ideal gas and the heat capacity С Р does not depend on temperature, relation (5.64) becomes (5.63). To solve equation (5.64), which describes a real gas, it is necessary to know the specific form of the dependence C p = f(T).

Isothermal process. Change in the internal energy of an ideal gas in a process occurring at a constant temperature

dU T = C V dT = 0. (5.65)

Adiabatic process. Since dU = C V dT, then for one mole of an ideal gas the change in internal energy and the work done are equal, respectively:

DU = C V dT = C V (T 2 - T 1); (5.66)

A fur = -DU = C V (T 1 - T 2). (5.67)

Analysis of equations characterizing various thermodynamic processes under the conditions: 1) p = const; 2) V = const; 3) T = const and 4) dQ = 0 shows that all of them can be represented general equation:

pV n = const. (5.68)

In this equation, the “n” indicator can take values ​​from 0 to ¥ for different processes:

1. isobaric (n = 0);

2. isothermal (n = 1);

3. isochoric (n = ¥);

4. adiabatic (n = g; where g = C P /C V – adiabatic coefficient).

The resulting relations are valid for an ideal gas and represent a consequence of its equation of state, and the processes considered are particular and limiting manifestations of real processes. Real processes, as a rule, are intermediate, occur at arbitrary values ​​of “n” and are called polytropic processes.

If we compare the work of expansion of an ideal gas produced in the considered thermodynamic processes with the change in volume from V 1 to V 2, then, as can be seen from Fig. 5.2, greatest work expansion occurs in an isobaric process, less in an isothermal process, and even less in an adiabatic process. For an isochoric process, the work is zero.

Rice. 5.2. P = f (V) – dependence for various thermodynamic processes (shaded areas characterize the work of expansion in the corresponding process)

Transport energy (cold transport) Air humidity. Heat capacity and enthalpy of air

Air humidity. Heat capacity and enthalpy of air

Atmospheric air is a mixture of dry air and water vapor (from 0.2% to 2.6%). Thus, the air can almost always be considered humid.

The mechanical mixture of dry air and water vapor is called moist air or an air-steam mixture. The maximum possible content of vaporous moisture in the air m p.n. depends on temperature t and pressure P mixtures. When it changes t And P the air can go from initially unsaturated to a state of saturation with water vapor, and then excess moisture will begin to fall into gas volume and on enclosing surfaces in the form of fog, frost or snow.

The main parameters characterizing the state of moist air are: temperature, pressure, specific volume, moisture content, absolute and relative humidity, molecular weight, gas constant, heat capacity and enthalpy.

According to Dalton's law for gas mixtures total pressure of moist air (P) is the sum of the partial pressures of dry air P c and water vapor P p: P = P c + P p.

Similarly, the volume V and mass m of moist air will be determined by the relations:

V = V c + V p, m = m c + m p.

Density And specific volume of moist air (v) defined:

Molecular weight of moist air:

where B is barometric pressure.

Since air humidity continuously increases during the drying process, and the amount of dry air in the steam-air mixture remains constant, the drying process is judged by how the amount of water vapor per 1 kg of dry air changes, and all indicators of the steam-air mixture (heat capacity, moisture content, enthalpy and etc.) refers to 1 kg of dry air located in moist air.

d = m p / m c, g/kg, or, X = m p / m c.

Absolute air humidity- mass of steam in 1 m 3 of moist air. This value is numerically equal to .

Relative humidity - is the ratio of the absolute humidity of unsaturated air to the absolute humidity of saturated air under given conditions:

here, but more often relative humidity is specified as a percentage.

For the density of moist air, the following relation is valid:

Specific heat humid air:

c = c c + c p ×d/1000 = c c + c p ×X, kJ/(kg× °C),

where c c is the specific heat capacity of dry air, c c = 1.0;

c p - specific heat capacity of steam; with n = 1.8.

The heat capacity of dry air at constant pressure and small temperature ranges (up to 100 o C) for approximate calculations can be considered constant, equal to 1.0048 kJ/(kg × ° C). For superheated steam average isobaric heat capacity at atmospheric pressure and low degrees of superheating can also be taken as constant and equal to 1.96 kJ/(kg×K).

Enthalpy (i) of moist air- this is one of its main parameters, which is widely used in calculations of drying installations, mainly to determine the heat spent on evaporating moisture from the materials being dried. The enthalpy of moist air is referred to one kilogram of dry air in a steam-air mixture and is determined as the sum of the enthalpies of dry air and water vapor, that is

i = i c + i p ×Х, kJ/kg.

When calculating the enthalpy of mixtures starting point the enthalpies of each component must be the same. For calculations of moist air, we can assume that the enthalpy of water is zero at 0 o C, then we also count the enthalpy of dry air from 0 o C, that is, i in = c in *t = 1.0048t.