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 the 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.

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).

Air density depending on temperature - table

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 reduction 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).

Dynamic and kinematic viscosity of air at different temperatures - table

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.

Specific heat capacity of air at different temperatures - table

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.

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 as humid.

The mechanical mixture of dry air and water vapor is called moist air or air/steam mixture. The maximum possible content of vaporous moisture in the air m a.s. temperature dependent 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 out in the gas volume and on the enclosing surfaces in the form of fog, hoarfrost or snow.

The main parameters characterizing the state of humid 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 wet air total pressure (P) is the sum of the partial pressures of dry air P c and water vapor P p: P \u003d P c + P p.

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

V \u003d V c + V p, m \u003d m c + m p.

Density and specific volume of humid air (v) defined:

Molecular weight of moist air:

where B is the barometric pressure.

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

d \u003d m p / m c, g / kg, or, X \u003d 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 the relative humidity is given as a percentage.

For the density of moist air, the relation is true:

Specific heat humid air:

c \u003d c c + c p ×d / 1000 \u003d c c + c p ×X, kJ / (kg × ° С),

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 ° C) for approximate calculations can be considered constant, equal to 1.0048 kJ / (kg × ° C). For superheated steam, the average isobaric heat capacity at atmospheric pressure and low degrees of superheat can also be assumed to be constant and equal to 1.96 kJ/(kg×K).

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

i \u003d i c + i p × X, kJ / kg.

When calculating the enthalpy of mixtures, the starting point of reference for the enthalpies of each of the components must be the same. For calculations of humid air, it can be assumed that the enthalpy of water is zero at 0 o C, then the enthalpy of dry air is also counted from 0 o C, that is, i in \u003d c in * t \u003d 1.0048t.

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 by 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 the 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 potentiometer 9. The heating of the air moving through the pipe is regulated 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 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 pressure;

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