The main physical properties of air are considered: air density, its dynamic and kinematic viscosity, specific heat capacity, thermal conductivity, thermal diffusivity, Prandtl number and entropy. The properties of air are given in tables depending on the temperature at normal atmospheric pressure.
Air density versus temperature
A detailed table of dry air density values at various temperatures and normal atmospheric pressure is presented. What is the density of air? The density of air can be analytically determined by dividing its mass by the volume it occupies. under given conditions (pressure, temperature and humidity). It is also possible to calculate its density using the ideal gas equation of state formula. To do this, you need to know the absolute pressure and temperature of the air, as well as its gas constant and molar volume. This equation allows you to calculate the density of air in a dry state.
On practice, to find out what is the density of air at different temperatures, it is convenient to use ready-made tables. For example, the given table of atmospheric air density values depending on its temperature. The air density in the table is expressed in kilograms per cubic meter and is given in the temperature range from minus 50 to 1200 degrees Celsius at normal atmospheric pressure (101325 Pa).
| t, °С | ρ, kg / m 3 | t, °С | ρ, kg / m 3 | t, °С | ρ, kg / m 3 | t, °С | ρ, kg / m 3 |
|---|---|---|---|---|---|---|---|
| -50 | 1,584 | 20 | 1,205 | 150 | 0,835 | 600 | 0,404 |
| -45 | 1,549 | 30 | 1,165 | 160 | 0,815 | 650 | 0,383 |
| -40 | 1,515 | 40 | 1,128 | 170 | 0,797 | 700 | 0,362 |
| -35 | 1,484 | 50 | 1,093 | 180 | 0,779 | 750 | 0,346 |
| -30 | 1,453 | 60 | 1,06 | 190 | 0,763 | 800 | 0,329 |
| -25 | 1,424 | 70 | 1,029 | 200 | 0,746 | 850 | 0,315 |
| -20 | 1,395 | 80 | 1 | 250 | 0,674 | 900 | 0,301 |
| -15 | 1,369 | 90 | 0,972 | 300 | 0,615 | 950 | 0,289 |
| -10 | 1,342 | 100 | 0,946 | 350 | 0,566 | 1000 | 0,277 |
| -5 | 1,318 | 110 | 0,922 | 400 | 0,524 | 1050 | 0,267 |
| 0 | 1,293 | 120 | 0,898 | 450 | 0,49 | 1100 | 0,257 |
| 10 | 1,247 | 130 | 0,876 | 500 | 0,456 | 1150 | 0,248 |
| 15 | 1,226 | 140 | 0,854 | 550 | 0,43 | 1200 | 0,239 |
At 25°C, air has a density of 1.185 kg/m 3 . When heated, the density of air decreases - the air expands (its specific volume increases). With an increase in temperature, for example, up to 1200°C, a very low air density is achieved, equal to 0.239 kg/m 3 , which is 5 times less than its value at room temperature. In general, the decrease in heating allows a process such as natural convection to take place and is used, for example, in aeronautics.
If we compare the density of air with respect to, then air is lighter by three orders of magnitude - at a temperature of 4 ° C, the density of water is 1000 kg / m 3, and the density of air is 1.27 kg / m 3. It is also necessary to note the value of air density under normal conditions. Normal conditions for gases are those under which their temperature is 0 ° C, and the pressure is equal to normal atmospheric pressure. Thus, according to the table, air density under normal conditions (at NU) is 1.293 kg / m 3.
Dynamic and kinematic viscosity of air at different temperatures
When performing thermal calculations, it is necessary to know the value of air viscosity (viscosity coefficient) at different temperatures. This value is required to calculate the Reynolds, Grashof, Rayleigh numbers, the values of which determine the flow regime of this gas. The table shows the values of the coefficients of dynamic μ and kinematic ν air viscosity in the temperature range from -50 to 1200°C at atmospheric pressure.
The viscosity of air increases significantly with increasing temperature. For example, the kinematic viscosity of air is equal to 15.06 10 -6 m 2 / s at a temperature of 20 ° C, and with an increase in temperature to 1200 ° C, the viscosity of the air becomes equal to 233.7 10 -6 m 2 / s, that is, it increases 15.5 times! The dynamic viscosity of air at a temperature of 20°C is 18.1·10 -6 Pa·s.
When air is heated, the values of both kinematic and dynamic viscosity increase. These two quantities are interconnected through the value of air density, the value of which decreases when this gas is heated. An increase in the kinematic and dynamic viscosity of air (as well as other gases) during heating is associated with a more intense vibration of air molecules around their equilibrium state (according to the MKT).
| t, °С | μ 10 6 , Pa s | ν 10 6, m 2 / s | t, °С | μ 10 6 , Pa s | ν 10 6, m 2 / s | t, °С | μ 10 6 , Pa s | ν 10 6, m 2 / s |
|---|---|---|---|---|---|---|---|---|
| -50 | 14,6 | 9,23 | 70 | 20,6 | 20,02 | 350 | 31,4 | 55,46 |
| -45 | 14,9 | 9,64 | 80 | 21,1 | 21,09 | 400 | 33 | 63,09 |
| -40 | 15,2 | 10,04 | 90 | 21,5 | 22,1 | 450 | 34,6 | 69,28 |
| -35 | 15,5 | 10,42 | 100 | 21,9 | 23,13 | 500 | 36,2 | 79,38 |
| -30 | 15,7 | 10,8 | 110 | 22,4 | 24,3 | 550 | 37,7 | 88,14 |
| -25 | 16 | 11,21 | 120 | 22,8 | 25,45 | 600 | 39,1 | 96,89 |
| -20 | 16,2 | 11,61 | 130 | 23,3 | 26,63 | 650 | 40,5 | 106,15 |
| -15 | 16,5 | 12,02 | 140 | 23,7 | 27,8 | 700 | 41,8 | 115,4 |
| -10 | 16,7 | 12,43 | 150 | 24,1 | 28,95 | 750 | 43,1 | 125,1 |
| -5 | 17 | 12,86 | 160 | 24,5 | 30,09 | 800 | 44,3 | 134,8 |
| 0 | 17,2 | 13,28 | 170 | 24,9 | 31,29 | 850 | 45,5 | 145 |
| 10 | 17,6 | 14,16 | 180 | 25,3 | 32,49 | 900 | 46,7 | 155,1 |
| 15 | 17,9 | 14,61 | 190 | 25,7 | 33,67 | 950 | 47,9 | 166,1 |
| 20 | 18,1 | 15,06 | 200 | 26 | 34,85 | 1000 | 49 | 177,1 |
| 30 | 18,6 | 16 | 225 | 26,7 | 37,73 | 1050 | 50,1 | 188,2 |
| 40 | 19,1 | 16,96 | 250 | 27,4 | 40,61 | 1100 | 51,2 | 199,3 |
| 50 | 19,6 | 17,95 | 300 | 29,7 | 48,33 | 1150 | 52,4 | 216,5 |
| 60 | 20,1 | 18,97 | 325 | 30,6 | 51,9 | 1200 | 53,5 | 233,7 |
Note: Be careful! The viscosity of air is given to the power of 10 6 .
Specific heat capacity of air at temperatures from -50 to 1200°С
A table of the specific heat capacity of air at various temperatures is presented. The heat capacity in the table is given at constant pressure (isobaric heat capacity of air) in the temperature range from minus 50 to 1200°C for dry air. What is the specific heat capacity of air? The value of specific heat capacity determines the amount of heat that must be supplied to one kilogram of air at constant pressure to increase its temperature by 1 degree. For example, at 20°C, to heat 1 kg of this gas by 1°C in an isobaric process, 1005 J of heat is required.
The specific heat capacity of air increases as its temperature rises. However, the dependence of the mass heat capacity of air on temperature is not linear. In the range from -50 to 120°C, its value practically does not change - under these conditions, the average heat capacity of air is 1010 J/(kg deg). According to the table, it can be seen that the temperature begins to have a significant effect from a value of 130°C. However, air temperature affects its specific heat capacity much weaker than its viscosity. So, when heated from 0 to 1200°C, the heat capacity of air increases only 1.2 times - from 1005 to 1210 J/(kg deg).
It should be noted that the heat capacity of moist air is higher than that of dry air. If we compare air, it is obvious that water has a higher value and the water content in the air leads to an increase in specific heat.
| t, °С | C p , J/(kg deg) | t, °С | C p , J/(kg deg) | t, °С | C p , J/(kg deg) | t, °С | C p , J/(kg deg) |
|---|---|---|---|---|---|---|---|
| -50 | 1013 | 20 | 1005 | 150 | 1015 | 600 | 1114 |
| -45 | 1013 | 30 | 1005 | 160 | 1017 | 650 | 1125 |
| -40 | 1013 | 40 | 1005 | 170 | 1020 | 700 | 1135 |
| -35 | 1013 | 50 | 1005 | 180 | 1022 | 750 | 1146 |
| -30 | 1013 | 60 | 1005 | 190 | 1024 | 800 | 1156 |
| -25 | 1011 | 70 | 1009 | 200 | 1026 | 850 | 1164 |
| -20 | 1009 | 80 | 1009 | 250 | 1037 | 900 | 1172 |
| -15 | 1009 | 90 | 1009 | 300 | 1047 | 950 | 1179 |
| -10 | 1009 | 100 | 1009 | 350 | 1058 | 1000 | 1185 |
| -5 | 1007 | 110 | 1009 | 400 | 1068 | 1050 | 1191 |
| 0 | 1005 | 120 | 1009 | 450 | 1081 | 1100 | 1197 |
| 10 | 1005 | 130 | 1011 | 500 | 1093 | 1150 | 1204 |
| 15 | 1005 | 140 | 1013 | 550 | 1104 | 1200 | 1210 |
Thermal conductivity, thermal diffusivity, Prandtl number of air
The table shows such physical properties of atmospheric air as thermal conductivity, thermal diffusivity and its Prandtl number depending on temperature. The thermophysical properties of air are given in the range from -50 to 1200°C for dry air. According to the table, it can be seen that the indicated properties of air depend significantly on temperature and the temperature dependence of the considered properties of this gas is different.
Which is necessary to change the temperature of the working fluid, in this case, air, by one degree. The heat capacity of air is directly dependent on temperature and pressure. At the same time, various methods can be used to study different types of heat capacity.
Mathematically, the heat capacity of air is expressed as the ratio of the amount of heat to the increment in its temperature. The heat capacity of a body having a mass of 1 kg is called the specific heat. The molar heat capacity of air is the heat capacity of one mole of a substance. The heat capacity is indicated - J / K. Molar heat capacity, respectively, J / (mol * K).
Heat capacity can be considered a physical characteristic of a substance, in this case air, if the measurement is carried out under constant conditions. Most often, such measurements are carried out at constant pressure. This is how the isobaric heat capacity of air is determined. It increases with increasing temperature and pressure, and is also a linear function of these quantities. In this case, the temperature change occurs at a constant pressure. To calculate the isobaric heat capacity, it is necessary to determine the pseudocritical temperature and pressure. It is determined using reference data.
Heat capacity of air. Peculiarities
Air is a gas mixture. When considering them in thermodynamics, the following assumptions were made. Each gas in the mixture must be evenly distributed throughout the volume. Thus, the volume of the gas is equal to the volume of the entire mixture. Each gas in the mixture has its own partial pressure, which it exerts on the walls of the vessel. Each of the components of the gas mixture must have a temperature equal to the temperature of the entire mixture. In this case, the sum of the partial pressures of all components is equal to the pressure of the mixture. Calculation of the heat capacity of air is performed on the basis of data on the composition of the gas mixture and the heat capacity of individual components.
Heat capacity ambiguously characterizes a substance. From the first law of thermodynamics, we can conclude that the internal energy of a body varies not only depending on the amount of heat received, but also on the work done by the body. Under different conditions of the heat transfer process, the work of the body may vary. Thus, the same amount of heat communicated to the body can cause changes in temperature and internal energy of the body that are different in value. This feature is characteristic only for gaseous substances. Unlike solids and liquids, gaseous substances can greatly change volume and do work. That is why the heat capacity of air determines the nature of the thermodynamic process itself.
However, at a constant volume, the air does not do work. Therefore, the change in internal energy is proportional to the change in its temperature. The ratio of the heat capacity in a constant pressure process to the heat capacity in a constant volume process is part of the adiabatic process formula. It is denoted by the Greek letter gamma.
From the history
The terms "heat capacity" and "amount of heat" do not describe their essence very well. This is due to the fact that they came to modern science from the theory of caloric, which was popular in the eighteenth century. The followers of this theory considered heat as a kind of imponderable substance contained in bodies. This substance can neither be destroyed nor created. The cooling and heating of bodies was explained by a decrease or increase in the caloric content, respectively. Over time, this theory was recognized as untenable. She could not explain why the same change in the internal energy of a body is obtained when transferring different amounts of heat to it, and also depends on the work done by the body.
Under specific heat substances understand the amount of heat that needs to be reported or subtracted from a unit of a 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 µC, referred to 1 kmole of gas, J/(kmol∙K);
Volumetric heat capacity WITH', referred to 1 m 3 of gas, J / (m 3 ∙K).
The specific heat capacities are interconnected by the relation:
where υ n- specific volume of gas under normal conditions (n.o.), m 3 /kg; µ - molar mass of gas, kg/kmol.
The heat capacity of an ideal gas depends on the nature of the process of supply (or removal) of heat, on the atomicity of the gas and temperature (the heat capacity of real gases also depends on pressure).
Relationship between mass isobaric C P and isochoric C V heat capacities is 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\u003d 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 mm Hg; T n- temperature under normal conditions, T n= 273.15K; P t, V t, T t– operating pressure, volume and temperature of the gas.
The ratio of isobaric heat capacity to isochoric is denoted k and call adiabatic exponent:
(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 that is required to heat or cool gases is often determined:
Q = Cm∙(t 2 - t 1), (1.8)
Q = C′∙V n∙(t 2 - t 1), (1.9)
where V n is the volume of gas at n.c., m 3 .
Q = µC∙ν∙(t 2 - t 1), (1.10)
where ν is the 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 the 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 with the help of a quantity measured experimentally.
The heat capacity of the system can serve as such a quantity. The most general definition of 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 in relation to the work of the form 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 capacity of the system;
P m and g m are, respectively, the generalized potential and the coordinate of the state of the form m.
The value C m shows how much work of the type m must be done under given conditions in order to change the m-th generalized potential of the system per unit of its measurement.
The concept of the capacity of a system with respect 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 with respect to heat is called the heat capacity and is given by the equality
C \u003d d e Q / dT \u003d Td e S warm / dT. (5.43)
In this way, heat capacity can be defined as the amount of heat that must be imparted to a system in order 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, and the heat capacity per mole of the substance, molar heat capacity. The specific heat capacity in SI is expressed in J/(kg·K), and the molar heat capacity is expressed in J/(mol·K).
The specific and molar heat capacities are related by the relation:
C mol \u003d C beat M, (5.44)
where M is the molecular weight of the substance.
Distinguish true (differential) heat capacity, determined from equation (5.43) and representing an elementary increase in 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 constant volume, then, in accordance with expression (5.27), the isochoric heat capacity C V is written as
C V = 
. (5.48)
If the system is heated at constant pressure, then, in accordance with equation (5.32), the isobaric heat capacity C P appears as
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 P - C V \u003d 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 expansion of the gas.
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 \u003d dU / dT \u003d d (3/2 RT) dT \u003d 3/2 R "12.5 J / (mol K); (5.53)
C Р \u003d 3 / 2R + R \u003d 5/2 R \u003e 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 the acceleration of translational motion. For polyatomic molecules, along with a change in the translational motion, a change in the rotational and vibrational intramolecular motion can also occur. For diatomic molecules, rotational motion is usually taken into account, as a result of which the numerical values of their heat capacities are:
C V \u003d 5/2 R "20.8 J / (mol K); (5.55)
C p \u003d 5/2 R + R \u003d 7/2 R \u003e 29.1 J / (mol K). (5.56)
In passing, we touch on the heat capacities of substances in other (except gaseous) aggregate states. 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 this compound. So, the heat capacity of a complex chemical compound, taking into account the Dulong and Petit rules, can be estimated as follows:
C V \u003d 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 (crystallization) temperature 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, the dependence of the heat capacity of solids on temperature in the range of 0 - 290K in most cases is well represented 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 coefficient of proportionality (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 that have the form of power series:
C P \u003d a + bT + cT 2 (5.59)
C P \u003d 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 method of heat capacities, let us write down some of the equations given in Section 5.1 in a slightly different form.
Isochoric process. Expressing the internal energy (5.27) in terms of heat capacity, we obtain
dU V \u003d dQ V \u003d U 2 - U 1 \u003d C V dT \u003d C V dT. (5.61)
Given that the heat capacity of an ideal gas does not depend on temperature, equation (5.61) can be written as follows:
DU V \u003d Q V \u003d U 2 - U 1 \u003d C V DT. (5.62)
To calculate the value of the integral (5.61) for real monatomic and polyatomic gases, it is necessary to know the specific form of the functional dependence C V = f(T) of the type (5.59) or (5.60).
isobaric process. For the gaseous state of matter, the first law of thermodynamics (5.29) for this process, taking into account the expansion work (5.35) and using the method of heat capacities, is written as follows:
Q P \u003d C V DT + RDT \u003d C P DT \u003d DH (5.63)
Q P \u003d DH P \u003d H 2 - H 1 \u003d C P dT. (5.64)
If the system is an ideal gas and the heat capacity C P 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 proceeding at a constant temperature
dU T = C V dT = 0. (5.65)
adiabatic process. Since dU \u003d 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)
And fur \u003d -DU \u003d C V (T 1 - T 2). (5.67)
Analysis of equations characterizing various thermodynamic processes under the following conditions: 1) p = const; 2) V = const; 3) T = const and 4) dQ = 0 shows that they can all be represented by the general equation:
pV n = const. (5.68)
In this equation, the exponent "n" 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 Р /C V is the adiabatic coefficient).
The relations obtained are valid for an ideal gas and are a consequence of its equation of state, and the considered processes are particular and limiting manifestations of real processes. Real processes, as a rule, are intermediate, proceed 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 a change in volume from V 1 to V 2, then, as can be seen from Fig. 5.2, the greatest work of expansion is performed in the isobaric process, the smallest - in the isothermal and even smaller - in the adiabatic. For an isochoric process, 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)
TEMPERATURE. It is measured in both Kelvin (K) and degrees Celsius (°C). The degree Celsius size and the kelvin size are the same for the temperature difference. Relationship between temperatures:
t = T - 273.15 K,
where t— temperature, °C, T— temperature, K.
PRESSURE. Humid air pressure p and its components is measured in Pa (Pascal) and multiple units (kPa, GPa, MPa).
barometric pressure of moist 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 moist 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 n /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 humid 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 to each other by dependence
ρ = γ /g,
where g— free fall acceleration, equal to 9.81 m/s 2 .
AIR HUMIDITY. The content of water vapor in the air. It is 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 pp contained in the air to the partial pressure of water vapor in the air when it is completely saturated with water vapor p b.s. :
φ \u003d (p p / p a.s.) 100%
The partial pressure of water vapor in saturated moist air can be determined from the expression
lg p a.s. \u003d 2.125 + (156 + 8.12t in.n.) / (236 + t in.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 humid air is equal to the partial pressure of saturated water vapor p a.s. at the same temperature. At dew temperature, condensation of moisture from the air begins.
d = M p / M in
d = 622p p / (p b - p p) = 6.22φp a.s. (p b - φp a.s. /100)
SPECIFIC HEAT. The specific heat capacity of moist air c, kJ / (kg * ° С) 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 the dry part of the air:
c \u003d c in + c p d / 1000,
where c to- the average specific heat 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
VOLUME EXPANSION COEFFICIENT. Temperature coefficient of volumetric expansion
α = 0.00367 °C -1
or α = 1/273 °C -1.
MIX PARAMETERS
.
Air mixture temperature
t cm \u003d (M 1 t 1 + M 2 t 2) / (M 1 + M 2)
d cm \u003d (M 1 d 1 + M 2 d 2) / (M 1 + M 2)
Specific enthalpy of air mixture
I cm \u003d (M 1 I 1 + M 2 I 2) / (M 1 + M 2)
where M1, M2— masses of mixed air
FILTERS CLASSES
| Application | Cleaning class | Cleaning degree | ||||
| Standards | DIN 24185 DIN 24184 |
EN 779 | EUROVENT 4/5 | EN 1882 | ||
| Coarse filter with low air cleanliness requirements | Rough cleaning | EU1 | G1 | EU1 | — | A% |
| Filter used at high concentrations of dust with coarse cleaning of it, Air conditioning and exhaust ventilation with low requirements for indoor air cleanliness. | 65 | |||||
| EU2 | G2 | EU2 | — | 80 | ||
| EU3 | G3 | EU3 | — | 90 | ||
| EU4 | G4 | EU4 | — | |||
| Separation of fine dust in ventilation equipment used in rooms with high requirements for air quality. Filter for very fine filtration. The second stage of cleaning (post-cleaning) in rooms with medium 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 of ultra-fine dust. It is used in rooms with increased requirements for air purity ("clean room"). Final air purification in rooms with precision technology, surgical units, resuscitation wards, in the pharmaceutical industry. | Extra fine cleaning | — | — | — | EU5 | WITH% |
| 97 | ||||||
| — | — | — | EU6 | 99 | ||
| — | — | — | EU7 | 99,99 | ||
| — | — | — | EU8 | 99,999 | ||
CALCULATION OF HEATER POWER
| Heating, °С | ||||||||||
| 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 REGULATORY DOCUMENTS
SNiP 2.01.01-82 - Construction climatology and geophysics
Information about the climatic conditions of specific territories.
SNiP 2.04.05-91* - Heating, ventilation and air conditioning
These 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, one should also comply with the requirements for heating, ventilation and air conditioning of the SNiP of the relevant buildings and premises, as well as departmental standards and other regulatory documents approved and agreed with the Gosstroy of Russia.
SNiP 2.01.02-85* - Fire regulations
These standards must be observed when developing projects for buildings and structures.
These standards establish the fire-technical classification of buildings and structures, their elements, building structures, materials, as well as general fire requirements for design and planning solutions for premises, buildings and structures for various purposes.
These standards are supplemented and specified by the fire safety requirements set forth in SNiP Part 2 and in other regulatory documents approved or agreed by Gosstroy.
SNiP II-3-79* – Building heat engineering
These norms of building heat engineering must be observed when designing enclosing structures (external and internal walls, partitions, coatings, 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 normalized temperature or temperature and relative humidity of the internal air).
SNiP II-12-77 - Noise protection
These norms and rules must be observed when designing noise protection to ensure acceptable sound pressure levels and sound levels in rooms at workplaces in production and auxiliary buildings and at 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 rules and regulations apply to the design of residential buildings (apartment buildings, including apartment buildings for the elderly and families with wheelchair users, hereinafter families with disabilities, as well as hostels) 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, one should additionally be guided by SNiP 2.08.01-89* (Residential buildings).
SNiP 2.09.04-87* - Administrative and residential buildings
These standards apply to the design of administrative and domestic buildings up to 16 floors inclusive and premises of enterprises. These standards do not apply to the design of administrative buildings and public premises.
When designing buildings 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 explosives, underground and mobile (inventory) buildings.
SNiP 111-28-75 - Rules for the production and acceptance of work
Start-up tests of the installed ventilation and air conditioning systems are carried out in accordance with the requirements of SNiP 111-28-75 "Rules for the production and acceptance of work" after mechanical testing of ventilation and related power equipment. The purpose of start-up tests and adjustment of ventilation and air conditioning systems is to establish the compliance of their operation parameters with design and standard indicators.
Prior to testing, ventilation and air conditioning installations must operate continuously and properly for 7 hours.
During start-up tests, the following must be carried out:
- Checking the compliance of the parameters of the installed equipment and elements of ventilation devices with those adopted in the project, as well as the compliance of the quality of their manufacture and installation with the requirements of TU and SNiP.
- Identification of leaks in air ducts and other elements of systems
- Verification of compliance with the design data of the volumetric flow rates of air passing through the air intake and air distribution devices of general exchange ventilation and air conditioning installations
- Checking compliance with passport data of ventilation equipment in terms of performance and pressure
- Checking the uniformity of heating of heaters. (In the absence of a coolant during the warm period of the year, the uniform heating of the heaters is not checked)
TABLE OF PHYSICAL VALUES
| Fundamental Constants | ||
| Constant (number) Avogadro | N A | 6.0221367(36)*10 23 mol -1 |
| Universal gas constant | R | 8.314510(70) J/(mol*K) |
| Boltzmann 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 | ft2 | 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 cm3 |
| 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 (US) | 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 cm3 |
| fluid ounce (US) | fl.oz (US) | 29.5737 cm3 |
| bushel (US) | bu (US) | 35.2393 dm 3 |
| dry barrel (US) | 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 / m 3) | ||
| pound per cubic foot | lb/ft3 | 16.0185 kg/m3 |
| 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 | 5/9K |
| Temperature (K) | ||
| Fahrenheit | °F | 5/9K; t°C = 5/9*(t°F - 32) |
| Force, weight (N or kg * m / s 2) | ||
| newton | H | 1 kg*m/s 2 |
| poundal | pdl | 0.1383H |
| pound-force | lbf | 4.4482H |
| kilogram-force | kgf | 9.807H |
| Specific gravity (N / m 3) | ||
| pound-force per cubic inch | lbf/ft3 | 157.087 H/m3 |
| 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 |
| physical atmosphere | atm | 1.013*10 5 N/m2 |
| millimeter of mercury | mm Hg | 1.333*10 2 N/m 2 |
| kilogram-force per cubic centimeter | kgf/cm3 | 9.807*10 4 N/m 2 |
| poundal per square foot | pdl/ft2 | 1.4882 N/m2 |
| pound-force per square foot | lbf/ft2 | 47.8803 N/m2 |
| pound-force per square inch | lbf/in2 | 6894.76 N/m2 |
| foot of water | ftH2O | 2989.07 N/m2 |
| inch of water | inH2O | 249.089 N/m2 |
| inch of mercury | in Hg | 3386.39 N/m2 |
| Work, energy, heat (J or kg * m 2 / s 2 or N * m) | ||
| joule | J | 1 kg * m 2 / s 2 \u003d 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 poundal | 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 |
| foot-pound-force 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 degree Fahrenheit | Btu/(s*ft 2 *degF) | 20441.7 W / (m 2 * K) |
| Thermal diffusivity, kinematic viscosity (m2/s) | ||
| stokes | St (st) | 10 -4 m 2 / s |
| centistokes | cSt (cSt) | 10 -6 m 2 / s \u003d 1 mm 2 / s |
| square foot per second | ft2/s | 0.0929 m2/s |
| Dynamic viscosity (Pa*s) | ||
| poise | P (P) | 0.1 Pa*s |
| centipoise cP | (cP) | 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 of water column | m 3 /(h * m * mm H 2 O) | 28.3255 * 10 -6 m 2 / (s * Pa) |
| The power of light | ||
| candela | cd | base SI 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
Lab #1
Definition of mass isobaric
air heat capacity
Heat capacity is the heat that must be supplied to a unit amount of a substance in order 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 a 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); volume c', 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 the molar heat capacity is not introduced. Relations between heat capacities:
where = 22.4 m3/kmol is the volume of a kilomole of an ideal gas under normal physical conditions; is the density of the gas 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 from the first law of thermodynamics for isochoric and isobaric processes:
Here, is the heat supplied to 1 kg of gas in the isobaric process; is the change in the internal energy of the gas; is the work of gases against external forces.
In essence, formula (4) formulates the 1st law of thermodynamics, from which the Mayer equation follows:
If we put = 1 K, then, that is, the physical meaning of the gas constant is the work of 1 kg of gas in an isobaric process when its temperature changes by 1 K.
Mayer's equation for 1 kilomole of gas is
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 interconnected through the adiabatic index 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 a reference value.
1.1. Description of the laboratory setup
The installation (Fig. 1.1) consists of a brass pipe 1 with an inner 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 controlled by changing the fan speed. In pipe 1, a tube of full pressure 4 and excess static pressure 5 are installed, 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 EMF value of the thermocouple is determined by the potentiometer 9. The heating of the air moving through the pipe is controlled using a laboratory autotransformer 12 by changing the heater power, which is determined by the readings of the ammeter 14 and voltmeter 13. The air temperature at the outlet of the heater is determined by the thermometer 15.
1.2. EXPERIMENTAL TECHNIQUE
Heat flow of the heater, W:
where I is current, A; U – voltage, V; = 0.96; =
= 0.94 - heat loss coefficient.
Fig.1.1. Scheme of the experimental setup:
1 - pipe; 2 - confuser; 3 – fan; 4 - tube for measuring dynamic head;
5 - branch 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 perceived by air, W:
where m is the 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 velocity in the pipe, m/s; d is the inner diameter of the pipe, m; - air density at temperature , which is found by the formula, kg/m3:
, (1.11)
where = 1.293 kg/m3 is the 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 head in four equal sections, m/s:
where is the dynamic head, mm. water. Art. (kgf/m2); g = 9.81 m/s2 is the free fall acceleration.
Average air velocity in the pipe section, m/s:
The average isobaric mass heat capacity of air is determined from formula (1.9), into which the heat flux is substituted from equation (1.8). The exact value of the heat capacity of air at an average air temperature is found according to the table of average heat capacities or according to 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 the stationary mode is established, the following readings are taken:
Dynamic air pressure at four points of equal sections of the pipe;
Excessive static air pressure in the pipe;
Current I, A and voltage U, V;
Inlet air temperature, °С (thermocouple 8);
Outlet temperature, °С (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
Value name | |||
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 head, N/m2 | ||||
Average inlet flow temperature, °C |
Loading...