Air humidity. Heat capacity and air enthalpy

The atmospheric air is a mixture of dry air and water vapor (from 0.2% to 2.6%). Thus, the air can almost always be viewed as wet.

Mechanical mixture of dry air with water vapor is called wet air or air-steam mixture. The maximum possible content of vapor moisture in the air m P.N. Depends on temperature t. and pressure P. Mixtures. When it changes t. and P. The air can move from the originally unsatisted in the saturation state with water vapors, and then the excessive moisture will begin to fall out in the gas volume and on the fencing surfaces in the form of fog, ina or snow.

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

By the Dalton Law for Gas Mixtures full pressure of wet air (P) There is the sum of partial pressures of dry air P C and water vapor p p: p \u003d p c + r.

Similarly, volume V and mass M wet air will be determined by the ratios:

V \u003d V C + V P, M \u003d M C + M p.

Density and specific volume of wet air (V) Determined:

Molecular weight of wet air:

where B is barometric pressure.

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

d \u003d m n / m C, g / kg, or, x \u003d m p / m c.

Absolute humidity- Course weight in 1 m 3 wet air. This value is numerically equal.

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

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

For wet air density, the ratio is true:

Specific heat Wet air:

c \u003d C + C P × D / 1000 \u003d C + C P × X, KJ / (kg × ° C),

where with C is the specific heat of dry air, with C \u003d 1.0;

with P - specific steam capacity; with n \u003d 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 a constant equal to 1.0048 kJ / (kg × ° C). For superheated steam, the average isobaric heat capacity at atmospheric pressure and low detection of overheating can also be made constant and equal to 1.96 kJ / (kg × K).

Entalpy (I) Wet Air - This is one of its main parameters, which is widely used in the calculations of the drying plants mainly to determine the heat consumed on the evaporation of moisture from the drying materials. Enhalar air enthalpy refer to one kilogram of dry air in the steam-air mixture and is determined as an amount of dry air enthalpy and water vapor, that is

i \u003d i c + i p × x, kj / kg.

When calculating the enthalpy of mixtures, the initial point of the enthalpium of each component should be the same. For calculations of wet air, it can be assumed that the enthalpy of water is zero at 0 ° C, then the enthalpy of dry air also count from 0 ° C, that is, I \u003d C * T \u003d 1.0048T.

Laboratory work number 1

The definition of mass isobarova

air heat capacity

The heat capacity is the heat that must be brought to a single amount of substance to heat it on 1 K. The unit amount of substance can be measured in kilograms, cubic meters under normal physical conditions and kilo moles. Kilome of gas is a mass of gas in kilograms, numerically equal to its molecular weight. Thus, there are three types of heatmakes: mass C, J / (kg⋅k); Volumenny with ', J / (M3⋅k) and Molna, J / (Cololk). Since the gas kilometer has a mass in μ times more than one kilogram, the individual notation for the molar heat capacity is not administered. Targets between heat circuits:

where \u003d 22.4 m3 / kmol - the volume of kilomol of the ideal gas under normal physical conditions; - Gas density under normal physical conditions, kg / m3.

The true heat capacity of the gas is derived from heat heat:

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

Here is the heat, which was supplied to 1 kg of gas in the isobaric process; - change in the internal energy of gas; - The operation of gases against external forces.

Essentially, formula (4) formulates the 1st beginning of thermodynamics, from where the Mayer equation is:

If we put \u003d 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 it changes its temperature by 1 K.

Mayer equation for 1 kilo praying gas has the appearance

where \u003d 8314 J / (Cololk) is a universal gas constant.

In addition to the Mayer equation, the isobaric and isochoric mass heat capacity of gases are interconnected through the adiabnity of K (Table 1):

Table 1.1.

Values \u200b\u200bof adiabatic indicators for perfect gases

PURPOSE OF THE WORK

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

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

1.1. Description of the laboratory installation

Installation (Fig. 1.1) consists of brass pipe 1 inner diameter D \u003d
\u003d 0.022 m, at the end of which the electrical insulation is located with thermal insulation 10. Inside the pipe, the air flow is moving, which is supplied 3. Air flow can be adjusted by changing the number of fan speed. In the pipe 1, the tube of complete pressure 4 and excess static pressure 5 is installed, which are connected to the pressure gauges 6 and 7. In addition, the thermocouple 8 is installed in the pipe 1, which can move along the cross section simultaneously with the full pressure tube. The magnitude of the EMF thermocouple is determined by the potentiometer 9. The heating of air moving along the pipe is adjusted using a laboratory vehicle 12 by changing the heater power, which is determined by the ammeter 14 and voltmeter readings 13. The air temperature at the outlet of the heater is determined by the thermometer 15.

1.2. Methodology for experiment

Heater thermal stream, W:

where i is current, and; U - voltage, in; \u003d 0.96; \u003d.
\u003d 0.94 - thermal loss coefficient.

Fig.1.1. Scheme of experimental installation:

1 - pipe; 2 - confusion; 3 - fan; 4 - tube for measuring dynamic pressure;

5 - nozzle; 6, 7 - dipmanometers; 8 - thermocouple; 9 - potentiometer; 10 - isolation;

11 - electric heater; 12 - Laboratory autotransformer; 13 - voltmeter;

14 - ammeter; 15 - Thermometer

Thermal flow, perceived by air, W:

where M is the mass flow of air, kg / s; - experimental, mass isobar heat capacity, J / (kg · k); - Air temperature at the outlet of the heating site 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 - the inner diameter of the pipe, m; - Air density at a temperature that is located according to the formula, kg / m3:

, (1.11)

where \u003d 1.293 kg / m3 - air density under normal physical conditions; B - pressure, mm. RT. st; - excess static air pressure in the pipe, mm. waters. Art.

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

where is the dynamic pressure, mm. waters. Art. (kgf / m2); G \u003d 9.81 m / s2 - Acceleration of free fall.

The average air velocity in the pipe cross section, m / s:

The average isobaric mass heat capacity is determined from formula (1.9), into which the heat flux is substituted from equation (1.8). The exact value of air heat capacity with an average air temperature is located on the table of medium heat capacity or by empirical formula, J / (kg⋅k):

. (1.14)

The relative error of the experiment,%:

. (1.15)

1.3. Experiment and processing

measurement results

The experiment is carried out in the following sequence.

1. The laboratory stand turns on and after establishing the stationary mode, the following readings are removed:

Dynamic air pressure at four points of isometric sections of the pipe;

Excess static air pressure in the pipe;

Current i, a and voltage u, in;

Air temperature at the entrance, ° 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 recorded in Table 1.2. Calculations are performed in Table. 1.3.

Table 1.2.

Table measurements

Table 1.3.

Table calculations

Purpose of work:determination of the isobar heat capacity of the air by the method of the flower calorimeter.

The task:

Experimentally determine the average volumetric isobaric heat capacity of air.

Based on the obtained experimental data, calculate the average mass and molar isobaric heat capacity and medium mass, volume and molar air heat capacity.

Determine the indiabator for air.

Compare the data obtained with tabular.

To estimate the accuracy of experimental data.

Basic provisions.

Heat capacity- The property showing how much heat must be brought to the system to change its temperature per degree.

In such a wording, the heat capacity makes the meaning of an extensive parameter, i.e. depending on the amount of substance in the system.

In this case, it is impossible to quantify the thermal properties of various materials, comparing them between themselves. For practical application, a much more informative parameter is the so-called specific heat.

Specific heatshows how the amount of heat must be brought to a unit of the amount of substance to heat it on one degree.

Depending on which units are measured by the amount of substance distinguish:

specific mass heat capacity (C). In the SI system measured in

;

Various types of specific heat consumption are interconnected:

,

where
- respectively specific mass, volumetric and molar heat capacity;

- gas density under normal physical conditions, kg / m 3;

- molar mass of gas, kg / kmol;

- The volume of one kilomol of the ideal gas under normal physical conditions.

In general, the heat capacity depends on the temperature at which it is determined.

The heat capacity defined at a given temperature value, i.e. When the change in the temperature of the system is currently striving for zero
, called true heat capacity.

However, the implementation of engineering calculations of heat exchange processes is substantially simplified, if we accept that when performing a process in the interval of changes in the temperature of the system from before the heat capacity does not depend on the temperature and remains constant. In this case, the so-called is accepted as the calculated average heat capacity.

Medium heat
- heat capacity constant in the temperature range interval from before .

The heat capacity depends on the nature of the heat supply process to the system. In the isobaric process, in order to heat the system for one degree, it is necessary to bring more heat than in isohorce. This is due to the fact that in the isobaric heat process, it is spent not only to change the internal energy of the system, as in a isochoretum process, but also to perform the system of operation of the volume.

In this regard distinguished isobaric
and izohorch
heat capacity, and the isobaric heat capacity is always more isochoret. The relationship between these types of heat capacity is determined by the formula of Mayer:

where - Gas constant, J / (kggrad).

In the practical application of this formula, it is necessary to be attentive to the correspondence of the dimension of values
,
and . In this case, for example, it is necessary to use a specific mass heat capacity. This formula will also be valid for other species of specific heat, but to avoid calculated errors, it is always necessary to pay attention to the correspondence of the dimensions of the values \u200b\u200bincluded in the formula. For example, when used instead universal gas constant the heat capacity should be a specific molar, etc.

In an isothermal process, all the warmth, summing up to the system, is spent on the execution of external work, and the internal energy and, therefore, the temperature does not change. The heat capacity of the system in such a process is infinitely large. In the adiabatic process, the temperature of the system changes without heat exchange with an external environment, which means that the system's heat capacity in such a process will be zero. For this reason there is no concepts of isothermal or adiabatic heat capacity.

In operation, a flowful calorimeter method is used to determine air heat capacity. The laboratory installation circuit is presented in Fig. 1.

Fig.1. Laboratory Stand Scheme

Air with a fan 1 is supplied to a calorimeter, which is a pipe 2 of the material with a low thermal conductivity and an outer thermal insulation 3 necessary to prevent thermal losses into the environment. Inside the calorimeter there is an electric heater 4. The heater power is carried out from the AC power through the voltage regulator 5. The power of the electric heater is measured by a wattmeter 6. To measure the air temperature at the inlet in the calorimeter and the output of it uses thermocouples 7 connected via a switch 8 to a device for measuring Thermo-EDC 9. Air flow through the calorimeter varies with a regulator 10 and is measured using a float rotation 11.

The procedure for performing work.

Get the source data and resolution of the head for work

Turn on the fan and set the specified air consumption.

Set the setpoint power of the electric heater.

After establishing a stationary temperature mode (controlled by the temperature sensor indications at the outlet of the calorimeter), the air temperature at the inlet and outlet of the calorimeter, air flow and the power of the heater are measured. Measurement results are recorded in the test table (see Table 1).

Table 1.

A new temperature is set and repeated measurements are carried out. Measurements must be performed at 2, 3 different modes.

After the measurement is completed, bring all regulators to the original state and turn off the installation.

According to the measurement results, the value of the average volumetric isobar air temperature is determined:

where
- The amount of heat supplied to the air in the calorimeter, W. It is taken equal to the value of the electrical power of the heater;

- respectively, the air temperature at the entrance to the calorimeter and the outlet of it, K;

- volume flow of air through the calorimeter, given to normal physical conditions, m 3 / s;

To bring the air consumption through the calorimeter to normal conditions, the equation of the state of the ideal gas recorded for normal physical conditions and the conditions of experience is used:

,

where in the left part of the air parameters at the entrance to the calorimeter, and in the right part - under normal physical conditions.

After finding values
corresponding to each of the mode studied, determines the value
which is assumed to estimate the experimental value of air heat capacity and is used in further calculations.

, kJ / kg;

The indiabator for air based on the relationship is determined

;

The obtained values \u200b\u200bof the isobaric and isochorean heat capacity are compared with table values \u200b\u200b(see Appendix 1) and estimate the accuracy of the experimental data obtained.

Results to put in Table 2.

Table 2.

CONTROL QUESTIONS.

What is called heat capacity?

What are the types of specific heat?

What is the average and true heat capacity?

What is called isobar and isochoretable heat? How are they interrelated?

Which of two heat dissimols are more: C P or C V and why? Explanation to give on the basis of the 1st law of thermodynamics.

Features of the practical application of the formula of Mayer?

Why do not have the concepts of isothermal and adiabatic heat capacity?

Attachment 1.

Air heat capacity depending on temperature

Study of the process of adiabatic gas expiration through a tapering nozzle.

purpose of work: Experimental and theoretical study of the thermodynamic characteristics of the gas expiration process from a tapering nozzle.

The task:

1. For a given gas, to obtain the dependence of the actual speed of expiration and consumption from the disposable pressure drop before and after the nozzle.

Basic provisions.

The thermodynamic study of gas flow processes through the channels has a great practical value. The main positions of the theory of gas expiration are used in the calculations of the running part of steam and gas turbines, jet engines, compressors, pneumatic drives and many other technical systems.

The channel of alternating section, when passing through which gas flow expands with a decrease in pressure and increase the speed, is called nozzle. In nozzles, there is a transformation of the potential energy of gas pressure into the kinetic energy of the stream. If there is an increase in the pressure of the working fluid and reducing the speed of its movement, then such a channel is called diffuser. In diffusers, an increase in the potential energy of gas is carried out by reducing its kinetic energy.

To simplify the theoretical description of the process of gas expiration, the following assumptions are accepted:

gas is ideal;

there is no internal friction in the gas, i.e. viscosity;

in the course of the expiration, there are no irreversible losses;

the gas flow is installed and stationary, i.e. At any point of the transverse section of the flow, the flow rate W M gas state parameters (P, V, T) are the same and do not change over time;

the course is one-dimensional, i.e. flow characteristics are changed only in the direction of flow flow;

there is no heat exchange between the stream and the external environment, i.e. The expiration process is adiabat.

The theoretical description of the process of gas expiration is based on the following equations.

The equation of the state of the ideal gas

,

where R - gas constant;

T- absolute gas flow temperature.

Adiabat Equation (Poisson Equation)

where P absolute gas pressure;

k- adiabat indicator.

Increteral equation of flow

where the f-area of \u200b\u200bthe cross section of the flow;

w- flow velocity;

v- Specific gas volume.

Bernoulli equation for the compressible working fluid, taking into account the absence of internal friction

This equation shows that with an increase in gas pressure, its speed and kinetic energy are always reduced, and vice versa, with a decrease in pressure, the speed and kinetic gas energy increase.

The equation of the 1st Law of Thermodynamics for Flow.

The 1st law of thermodynamics in the general case has the following form

,

where
- elementary amount of heat supplied to the system;

- elementary change in the internal energy of the system;

- Elementary operation of changes in the volume performed by the system.

In the case of a movable thermodynamic system (the flow of a moving gas), a part of the operation of the volume changes is spent on overcoming the forces of external pressure, i.e. Actually on moving gas. This part of the general work is called work pushing. The remaining part of the operation of the volume changes can be used useful, for example, is spent on the rotation of the turbine wheel. This part of the overall work of the system is called disposable or technical work.

Thus, in the case of a gas flow, the operation of changes in volume consists of 2 components - work of pushing and technical (disposable) work:

where
- elementary work of pushing;

- elementary technical work

Then the 1st law of thermodynamics for the flow will be

,

where
- Elementary change in enthalpy system.

In case of adiabatic expiration

Thus, when adiabat expiration technical work is made due to the decrease of enthalpy gas.

Based on the assumptions discussed above for the case of gas expiration from an unlimited capacity vessel (the initial gas velocity
) Formulas are obtained to determine theoretical speed and mass gas flow in the weekend of the nozzle:

or

where
- pressure and gas temperature in the input section of the nozzle;

- specific enthalpy of flow, respectively, at the entrance to the nozzle and outlet of the nozzle;

- Indicator adiabat;

- gas constant;

- the ratio of pressures at the exit of the nozzle and at the entrance to the nozzle;

- Output area of \u200b\u200bthe nozzle.

The analysis of the obtained formulas shows that according to the theory of the theory of theoretical velocity and mass flow rate from the pressure ratio, it is olive to be the form submitted on the graphs with curves marked with the letter T (see Fig. 1 and Fig. 2). It follows from the graphs that according to the theory with a decrease in values \u200b\u200b1 to 0, the rate of expiration should continuously increase (see Fig. 1), and the mass flow rate first increases to a certain maximum value, and then should decrease up to 0 at \u003d 0 ( See Fig.2).

Fig. 1. The dependence of the rate of expiration of pressure ratio 

Fig. 2. The dependence of the mass flow rate of pressure ratio 

However, with an experimental study of the expiration of gases from a narrowing nozzle, it was found that with a decrease of 1 to 0, the actual expiration rate and, accordingly, the actual consumption increases in full compliance with the accepted process theory, but after reaching the maximum of their values, with further decrease to 0 remain unchanged

The nature of these dependencies is shown on the graphs with curves marked with the letter D (see Fig. 1 and Fig.2).

The physical explanation of the discrepancy of theoretical dependence with experimental data was first proposed in 1839 by the French scientist Saint-Venne. It was confirmed by further research. It is known that any, even a weak perturbation of a fixed medium spreads in it at the speed of sound. In the stream moving through the nozzle towards the source of the perturbation, the rate of transmission of perturbation inside the nozzle, i.e. Against the direction of flow movement will be below the speed of the stream itself. This is the so-called relative rate of spread of indignation, which is equal
. When the wave of perturbation is passed inside the nozzle along the entire flow, the corresponding redistribution of pressures occurs, the result of which according to the theory is an increase in the rate of expiration and gas flow rate. With a constant pressure of the gas at the inlet in the nozzle 1 \u003d concent of the pressure of the medium in which gas flows, a decrease in the value of β corresponds.

However, if the pressure of the medium in which gas flows will decrease to a certain value, in which the expiration rate at the outlet from the nozzle will become equal to the local sound velocity, the perturbation wave will not be able to spread the inside of the nozzle, since the relative speed of its propagation in the direction opposite to the movement will be zero:

.

In this regard, the redistribution of pressure in the stream along the nozzle will not be able to occur, the rate of gas expiration at the outlet of the nozzle will remain unchanged and equal to local sound velocity. In other words, the flow as if "blows out" the cut from the nozzle created outside. How much would not be reduced further the absolute pressure of the medium for the nozzle of further increasing the rate of expiration, and therefore the consumption will not happen, because Figuratively speaking, according to Reynolds, "nozzle ceases to feel what happens beyond" or how sometimes they say "nozzle is locked." Some analogy of this phenomenon is the situation that can sometimes be observed when the sound of a person's voice is demolished by the strength of a strong oncoming wind and his words the interlocutor cannot hear, being even completely close if the wind blows from him to ever the speaker.

The expiration mode, in which the expiration rate at the outlet of the nozzle reaches the local sound speed, is called critical regime.Explicit rate , flow and pressure ratio corresponding to this regime are also called critical. This mode corresponds to the maximum values \u200b\u200bof the expiration rate and consumption, which can be achieved when the gas expires through the usual tapering nozzle. The critical pressure ratio is determined by the formula

,

where k- indicator of adiabat.

The critical point of pressure depends only on the genus of the gas and for a particular gas is constant. For example:

for single-varia gases k \u003d 1.66 and  0.489;

for 2 atomic gases and air k \u003d 1.4 and  to 0,528

for 3 and polyhydric gases k \u003d 1.3 and  to 0,546.

Thus, theoretical dependencies to determine the rate of expiration and consumption of gas obtained in the framework of adopted assumptions are in reality only in the field of values
. At values
the rate of expiration and consumption in reality remain constant and maximum for these conditions.

Moreover, for the actual conditions of movement of the flow, the actual expiration rate and gas flow rate at the outlet of the nozzle even at the values
will be slightly lower than theoretical values \u200b\u200bcorresponding to them. This is due to the friction of the jet about the wall of the nozzle. The temperature at the outlet of the nozzle is somewhat higher than theoretical temperature. This is due to the fact that a portion of the disposable operation of the gas flow dissipates and turns into heat, which leads to an increase in temperature.

Description of the laboratory stand.

The study of the gas expiration process from the nozzle is carried out at the installation based on the method of simulation modeling of real physical processes. The installation consists of a PEVM connected to the working port model, a control panel and measurement tools. The installation scheme is presented in Fig.3.

Fig.3. Installation scheme to study the gas expiration process

The working section of the installation is a tube in which the suspended tousing nozzle 3 is installed with an output diameter D \u003d 1.5 mm. The gas flow (air, carbon dioxide (CO 2), helium (HE)) is created through a nozzle using a vacuum pump 5. The gas pressure at the inlet is equal to barometric pressure (P 1 \u003d b). Gas Consumption The speed of expirations will adjust the valve 4. The operating modes are determined by the resolution value for the nozzle 3, which is recorded on the digital indicator 6. Gas consumption is measured using a measuring diaphragm diameterd d \u003d 5 mm. The pressure difference on the diaphragm "is registered on the digital indicator 7 and is duplicated on the PEVM monitor screen. The pouringp 2 in the output section of the nozzle is also recorded on the digital indicator 6 and the monitor screen. The flow rate coefficient of the measuring diaphragm with the calibrated hole \u003d 0.95 is determined as a result of the targeting.

The procedure for performing work.

Include installation to the network, join a dialog with a program of the experiment embedded in the computer.

Choose a gas supply for the experiment.

Enable vacuum pump. This creates a vacuum for the valve 4, which is displayed on the monitor screen.

The gradual opening of the valve 4 is set minimum vacuum

P 3 \u003d 0.1 AT, which corresponds to the 1st regime. At the same time, the flow of gas begins.

Make a protocol of the experiment (Table 1) numeric values \u200b\u200bof P 3, P 2, h, fixed by digital indicators 6 and 7.

Perform the measurements of the values \u200b\u200bof p 2, Hlam subsequent modes corresponding to the values \u200b\u200bof the vacuum pump created by the vacuum pump,

p 3 \u003d 0.2; 0.3; 0.4; 0.5 .....0.9 at. Measurement results add to Table 1

Table 1.

Gas pressure at the inlet into nozzle p 1 \u003d b \u003d pa.

Gas temperature at the inlet in nozzle T 1 \u003d C.

Processing measurement results.

The absolute pressure of the medium P 3 is determined per nozzle into which the gas is expired.

, PA

4.2. The absolute pressure of the gas P 2 is determined in the output section of the nozzle

, PA

The valid mass flow rate of gas in terms of pressure drop is determined by a measuring diaphragm

, kg / s

where
- Flow coefficient of the measuring diaphragm;

- pressure drop on the measuring diaphragm, pa;

- gas density, kg / m 3;

- barometric pressure, PA;

- Gas constant, J / (kg ∙ hail);

- gas temperature, c;

- diameter of the measuring diaphragm.

4.4. Since the expiration process is adiabat, the theoretical temperature of the gas T 2 is determined on the nozzle section, using a known ratio for the adiabatic process:

4.5. The actual expiration rate is determined and gas temperature in the weekend of the nozzle

, m / s;

where - valid mass flow rate, kg / s;

- respectively, the temperature (K) and the pressure (PA) of the gas in the output cross section of the nozzle;

- area of \u200b\u200bthe output snot;

- The diameter of the output section of the nozzle.

On the other hand, on the basis of the 1st Law of Thermodynamics for Flow

where
- Gas specific enthalpy, respectively, at the entrance and outlet of the nozzle, J / kg;

- gas temperature, respectively, at the entrance and outlet of the nozzle, K;

- Specific isobaric heat capacity, J / (kggrad);

Equating the right-wing parts of equations (17) and (18), and solving the resulting square equation relative to T 2, the actual gas temperature in the outlet cross section of the nozzle is determined.

or

,

where
;

;

.

4.6. The theoretical mass consumption of gas under adiabatic expiration is determined.

, kg / s;

where - the area of \u200b\u200bthe output section of the nozzle, m 2;

- absolute gas pressure at the entrance to the nozzle, PA;

- gas temperature at the entrance to the nozzle, K;

- Gas constant, J / (kggrad);

- Indicator adiabat.

4.7. The theoretical rate of gas expiration is determined

where - gas temperature in the input section of the nozzle;

- Indicator adiabat;

- gas constant;

- the ratio of pressures;

- the absolute pressure of the medium into which the gas is expiiled, PA;

- Absolute gas pressure at the entrance to the nozzle, PA.

4.8. The maximum theoretical rate of gas expiration is determined
(Expiration into the emptiness of the P 3 \u003d 0) and the local theoretical speed of the sound (critical speed)
.

4.9. The results of the calculations are recorded in Table 2.

Table 2.

4.10. In coordinates
and
dependence graphs are built, and a dependency schedule is built
. By schedules, the value of the critical pressure ratio is determined. ,

which is compared with the calculated

.

4.11. According to the results of computing and graphic buildings, make a conclusion about the following:

How dependes the theoretical rate of expiration and gas flow rate from the pressure ratio β?

How do the actual expiration rate and gas consumption depend on the pressure ratio β?

Why values \u200b\u200bof valid expiration speed and gas flow rate below appropriate theoretical values \u200b\u200bwith the same external conditions?

CONTROL QUESTIONS.

What assumptions are accepted in the theoretical description of the thermodynamics of the gas expiration process?

What basic laws are used for theoretical description of the expiration process?

What components are the work performed by a gas flow, when exposeding through the nozzle?

What is the connection between the enthalpy and the technical operation of the gas flow during the adiabatic expiration?

What is the critical expiration mode and what is it characterized?

How to explain from a physical point of view the discrepancy between theoretical and experimental dependences of the expiration rate and expense from ?

How do the actual conditions for the expiration on speed, consumption and temperature of gas at the exit of the nozzle?

Which is necessary to change the temperature of the working fluid, in this case, air, one degree. The heat capacity of the air directly depends on temperature and pressure. At the same time, various methods can be used to study different types of heat capacity.

Mathematically, air heat capacity is expressed as the ratio of the amount of heat to the increment of its temperature. The heat capacity of the body having a mass of 1 kg is customary to be called specific. The molar heat capacity of air is the heat capacity of one praying matter. Designated heat capacity - J / K. Molar heat capacity, respectively, J / (mol * k).

The heat capacity can be considered a physical characteristic of any substance, in this case of 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 an increase in temperature and pressure, and is also a linear function of these values. In this case, the temperature change occurs at constant pressure. To calculate the isobaric heat capacity, it is necessary to determine the pseudocritic temperature and pressure. It is determined using reference data.

Air heat capacity. Features

Air is a gas mixture. When consideration, the following assumptions were taken in thermodynamics. Each gas in the composition of the mixture should be evenly distributed throughout the volume. Thus, the volume of gas is equal to the volume of the whole mixture. Each gas in the composition of the mixture has its partial pressure, which it renders on the walls of the vessel. Each of the components of the gas mixture should have a temperature equal to the temperature of the entire mixture. In this case, the sum of partial pressures of all components is equal to the pressure of the mixture. The calculation of air heat capacity is carried out on the basis of data on the composition of the gas mixture and the heat capacity of individual components.

The heat capacity ambiguously characterizes the substance. Of the first law of thermodynamics, it can be concluded that the internal energy of the body varies not only depending on the amount of heat obtained, but also from the perfect body of work. Under different conditions of the heat transfer process, the body work may vary. Thus, the same reported body is the amount of heat, can cause various in the meaning of temperature change and internal body energy. This feature is characteristic only for gaseous substances. Unlike solid and liquid bodies, gaseous substances can strongly change the volume and work. That is why the heat capacity of air defines the nature of the thermodynamic process itself.

However, with a constant volume, the air does not work. Therefore, the change in internal energy is proportional to the change in its temperature. The ratio of heat capacity in a constant pressure process, to heat capacity in the process with a constant volume is part of the formula of the adiabatic process. It is indicated by the Gampea Gamma Literary.

From the history

The terms "heat capacity" and "the amount of heat" do not well describe their essence. This is due to the fact that they came into modern science from the theory of heator plant, which was popular in the eighteenth century. The followers of this theory were considered warmth as a kind of weightless substance, which is contained in bodies. This substance cannot be destroyed or created. Cooling and heating of bodies were explained by a decrease in or increasing the heat vehicle content, respectively. Over time, this theory was invalid. She could not explain why the same change in the internal energy of any body is obtained by transmitting it a different amount of warmth, and also depends on the body performed by the body.