Heat capacity definition in physics. Brief theoretical information

The change in internal energy by doing work is characterized by the amount of work, i.e. work is a measure of the change in internal energy in this process. The change in the internal energy of a body during heat transfer is characterized by a quantity called the amount of heat.

is a change in the internal energy of a body during the process of heat transfer without performing work. The amount of heat is indicated by the letter Q .

Job, internal energy and the amount of heat are measured in the same units - joules ( J), like any type of energy.

In thermal measurements, a special unit of energy was previously used as a unit of heat quantity - the calorie ( feces), equal to the amount of heat required to heat 1 gram of water by 1 degree Celsius (more precisely, from 19.5 to 20.5 ° C). This unit, in particular, is currently used when calculating heat consumption (thermal energy) in apartment buildings. The mechanical equivalent of heat has been experimentally established - the relationship between calorie and joule: 1 cal = 4.2 J.

When a body transfers a certain amount of heat without doing work, its internal energy increases; if the body gives off a certain amount of heat, then its internal energy decreases.

If you pour 100 g of water into two identical vessels, one and 400 g into the other at the same temperature and place them on identical burners, then the water in the first vessel will boil earlier. Thus, than more mass body, so more it needs heat to warm up. It's the same with cooling.

The amount of heat required to heat a body also depends on the type of substance from which the body is made. This dependence of the amount of heat required to heat a body on the type of substance is characterized by a physical quantity called specific heat capacity substances.

- This physical quantity, equal to the amount of heat that must be imparted to 1 kg of a substance to heat it by 1 ° C (or 1 K). 1 kg of substance releases the same amount of heat when cooled by 1 °C.

Specific heat capacity is designated by the letter With. The unit of specific heat capacity is 1 J/kg °C or 1 J/kg °K.

The specific heat capacity of substances is determined experimentally. Liquids have a higher specific heat capacity than metals; Water has the highest specific heat, gold has a very small specific heat.

Since the amount of heat is equal to the change in the internal energy of the body, we can say that the specific heat capacity shows how much the internal energy changes 1 kg substance when its temperature changes by 1 °C. In particular, the internal energy of 1 kg of lead increases by 140 J when heated by 1 °C, and decreases by 140 J when cooled.

Q = c ∙ m (t 2 - t 1)

The same formula is used to calculate the amount of heat that a body gives off when cooling. Only in this case should the final temperature be subtracted from the initial temperature, i.e. from greater value subtract the lesser temperature.

This is a summary of the topic “Amount of heat. Specific heat". Choose what to do next:

• Go to next summary:

Heat capacity of the body is a physical quantity determined by the ratio of the amount of heat absorbed by a body when heated to the change in its temperature:

The physical meaning of the heat capacity of a body: the heat capacity of a body is equal to the amount of heat absorbed by the body when heated or released when it is cooled by 1K.

Since heat capacities are variable, a distinction is made between average and true heat capacities. The average heat capacity is the ratio of the amount of heat q , added to a unit amount of a substance (gas), to a change in its temperature from t 1 to t 2 provided that the temperature difference t 2 –t 1 is a finite quantity. The average mass, volume and molar heat capacities are respectively denoted by c m , c m ' And m . From the definition of average heat capacity it follows that if the gas temperature increases from t 1 to t 2 then its average heat capacity [kJ/(kg*K)]

True heat capacity is understood as the heat capacity of a gas corresponding to an infinitesimal change in the temperature of the gas, corresponding to an infinitesimal change in temperature dt , i.e.

c = dq/dt,

where dq = cdt.

Specific heat- this is the ability of different substances to absorb heat when heated. The specific heat capacity of a substance is determined by the ratio of the amount of heat it receives when heated to the mass of the substance and the change in its temperature, if:

the relationship expressing the relationship between the molar heat capacities Cp and CV has the form (Mayer’s formula): Cp = CV + R. OR MORE EXPANDED Heat capacity of an ideal gas If, as a result of heat exchange, a certain amount of heat is transferred to the body, then the internal energy of the body and its temperature change. The amount of heat Q required to heat 1 kg of a substance by 1 K is called the specific heat capacity of the substance c. c = Q / (mΔT). In many cases it is convenient to use the molar heat capacity C: C = M c, where M is molar mass substances. The heat capacity determined in this way is not an unambiguous characteristic of a substance. According to the first law of thermodynamics, the change in the internal energy of a body depends not only on the amount of heat received, but also on the work done by the body. Depending on the conditions under which the heat transfer process was carried out, the body could perform various jobs. Therefore, the same amount of heat transferred to a body could cause different changes in its internal energy and, consequently, temperature. This ambiguity in determining heat capacity is typical only for gaseous substances. When liquids and solids are heated, their volume practically does not change, and the work of expansion turns out to be zero. Therefore, the entire amount of heat received by the body goes to change its internal energy. Unlike liquids and solids, gas can greatly change its volume and do work during heat transfer. Therefore, the heat capacity of a gaseous substance depends on the nature of the thermodynamic process. Usually two values ​​of the heat capacity of gases are considered: CV – molar heat capacity in an isochoric process (V = const) and Cp – molar heat capacity in an isobaric process (p = const). In the process at a constant volume, the gas does no work: A = 0. From the first law of thermodynamics for 1 mole of gas it follows QV = CVΔT = ΔU. The change ΔU of the internal energy of a gas is directly proportional to the change ΔT of its temperature. For the process at constant pressure the first law of thermodynamics gives: Qp = ΔU + p(V2 – V1) = CVΔT + pΔV, where ΔV is the change in the volume of 1 mole of an ideal gas when its temperature changes by ΔT. It follows: The ratio ΔV / ΔT can be found from the equation of state of an ideal gas, written for 1 mole: pV = RT, where R is the universal gas constant. At p = const Thus, the relationship expressing the relationship between the molar heat capacities Cp and CV has the form (Mayer’s formula): Cp = CV + R.

The gas constant is numerically equal to the work of expansion of 1 mole of an ideal gas under constant pressure when heated by 1 K. R = pV/T = 1.01 10 5 22.4 10-3/273[Pa m 3 /mol]/K = 8.31(44) Dl/ (mol K)

The universal gas constant is a universal, fundamental physical constant R, equal to the product of Boltzmann's constant k and Avogadro's constant

Physical meaning: Gas constant i is numerically equal to the work of expansion of one mole of an ideal gas in an isobaric process with an increase in temperature by 1 K

In the GHS system, the Gas constant is equal to:

The specific gas constant is equal to:

Adiabatic exponent(sometimes called coefficientPoisson) - the ratio of heat capacity at constant pressure () to heat capacity at constant volume (). Sometimes it is also called factor isentropic extensions. Designated Greek letter(gamma) or (kappa). The letter symbol is primarily used in chemical engineering disciplines. In heat engineering, the Latin letter is used.

A mixture of gases is a collection of several dissimilar gases that, under the conditions under consideration, do not enter into chemical reactions with each other.

A mixture of gases is a homogeneous thermodynamic system (within which there are no interfaces separating macroscopic parts of the system from each other, differing in their properties and composition).

Partial pressure The Pi of the i-th gas in a mixture is the pressure under which this gas would be if all other gases were removed from the mixture, and V and T remained the same.

Dalton's law - The pressure of a mixture of gases that do not interact chemically with each other is equal to the sum of the partial pressures of these gases.

In order to understand what it is Dalton's law, let's consider the air in the room for this. It is a mixture of several gases: nitrogen (80%), oxygen (20%). The partial pressure of each of these gases is the pressure that the gas would have if it alone occupied the entire volume. For example, if all gases except nitrogen were removed from a room, the pressure of what remained would be the partial pressure of nitrogen. Dalton's law states that total pressure of all gases taken together is equal to the sum of the partial pressures of each gas separately. (Strictly speaking, the law applies only to ideal gases, but to a fairly good approximation it also describes real gases.)

First law of thermodynamics is a generalization of the law of conservation and transformation of energy for thermodynamic system. It is formulated as follows:

Change ΔU internal energy of a non-isolated thermodynamic system is equal to the difference between the amount of heatQ , transferred to the system, and the workA , a perfect system over external bodies.

The relationship expressing the first law of thermodynamics is often written in a different form:

The amount of heat received by the system goes to change its internal energy and perform work on external bodies.

The first law of thermodynamics is a generalization of experimental facts. According to this law, energy cannot be created or destroyed; it is transmitted from one system to another and transformed from one form to another. An important consequence The first law of thermodynamics is a statement about the impossibility of creating a machine capable of performing useful work without consuming energy from the outside and without any changes within the machine itself. This hypothetical machine was called perpetual motion machine (perpetuum mobile) of the first kind . Numerous attempts to create such a machine invariably ended in failure. Any machine can do positive work A above external bodies only due to the receipt of a certain amount of heat Q from surrounding bodies or decreasing Δ U your internal energy.

Let us apply the first law of thermodynamics to isoprocesses in gases.

IN isochoric process (V= const) the gas does not do any work, A= 0. Therefore,

The first law of thermodynamics for an isobaric process gives:

Q = U (T 2) – U (T 1) + p (V 2 – V 1) = Δ U + p Δ V.

1. With isobaric expansion Q> 0 – heat is absorbed by the gas, and the gas does positive work. Under isobaric compression Q < 0 – тепло отдается внешним телам. В этом случае A < 0. Температура газа при изобарном сжатии уменьшается, T 2 < T 1 ; internal energy decreases, Δ U < 0.

   IN isothermal process the temperature of the gas does not change, therefore, the internal energy of the gas, Δ, does not change either U = 0.

The first law of thermodynamics for an isothermal process is expressed by the relation

Amount of heat Q, obtained by the gas during the process of isothermal expansion, turns into work on external bodies. During isothermal compression, work external forces, produced over the gas, turns into heat, which is transferred to surrounding bodies.

Along with isochoric, isobaric and isothermal processes, thermodynamics often considers processes that occur in the absence of heat exchange with surrounding bodies. Vessels with heat-tight walls are called adiabatic shells, and the processes of expansion or compression of gas in such vessels are called adiabatic.

IN adiabatic processQ= 0; therefore the first law of thermodynamics takes the form

Internal body energy- the sum of the kinetic energy of the chaotic movement of molecules relative to the center of mass of the body and the potential energy of interaction of molecules with each other (but not with molecules of other bodies). Depends on temperature and volume.

We can change the energy of the body by doing work on it. For example, when inflating a bicycle tire, the pump heats up. Some people think that due to the fact that the piston rubs against the walls of the pump, and the reason for this is that we compress the gas, we do work on it, which goes towards increasing the internal energy and this manifests itself as an increase in temperature.

There is another way to change the internal energy of a body without doing work - heat transfer.

Heat transfer

Heat transfer- a method of transferring the internal energy of the body without doing work.

Heat transfer can be transferred in three ways:

• thermal conductivity;
• convection;
• radiation (radiation);

These three ways can change the internal energy of the body.

The combination of all types of heat transfer is called complex heat transfer. Heat transfer processes can occur in different environments: pure substances with or without a change in the aggregate state of working media, etc. Depending on this, heat transfer proceeds differently and is described by different equations.

Thermal conductivity

The process of heat transfer by thermal conductivity occurs through direct contact of bodies or particles of bodies with different temperatures and is a molecular process of heat transfer due to the vibration of molecules. Molecules with a larger vibration amplitude cause neighboring molecules with a smaller vibration amplitude to vibrate more frequently.

When the body heats up kinetic energy its molecules increases, and particles of the hotter part of the body, colliding with neighboring molecules, impart to them part of their kinetic energy. In this case, the hotter parts of the body cool down, and the less heated ones heat up.

Convection

Convection is the transfer of heat when moving or mixing the entire mass of unevenly heated liquids or gases. In this case, heat transfer depends on the speed of movement of the liquid or gas in direct proportion.

Convective heat transfer- simultaneous heat transfer by convection and thermal conductivity. In engineering calculations, convective heat transfer between liquid or gas flows and a surface is often determined. solid. This process of convective heat transfer is called convective heat transfer or simply heat transfer.

Radiation

Radiation ( thermal radiation, radiation) is the process of transferring heat to the internal energy of a body in the form electromagnetic waves.

This process occurs in three stages:

• conversion of part of the internal energy of one body into the energy of electromagnetic waves;
• propagation of electromagnetic waves in space;
• absorption of radiation energy by another body.

Radiation-conduction heat transfer- joint heat exchange by radiation and thermal conductivity.

Amount of heat

Quantity of heat (Q)- the energy imparted to the body during the process of heat transfer is called the amount of heat and is measured in [J].

If physical state substance does not change (does not change potential energy interaction of molecules with each other, and the kinetic one changes), then the change in internal energy is associated with a change in internal temperature.

Q ~ ΔT
The amount of heat received is directly proportional to the difference in body temperature.

The proportionality coefficient depends on the body, mass and volume and is a characteristic of the body. If we take a glass of water and increase the temperature by 1 Kelvin, then we need one amount of heat. If we take the sea, then we will need a completely different amount of heat.

Q = СΔТ
C is the heat capacity of the body.

Heat capacity of the body- a physical quantity numerically equal to the amount of heat that the body needs to communicate to increase its temperature by 1 Kelvin.

Specific heat

The heat capacity of a body depends directly on the mass of the body, i.e. this is a property of matter.

C = cm, с=С/m, [c] = [J/kg*K]
C is the specific heat capacity (heat capacity of the substance).

Accordingly, the formula for the amount of heat can be written in the following form.

Q = cmΔТ
c is the heat capacity of the substance
m - body weight
ΔT - temperature difference

Specific heat substances- a physical quantity numerically equal to the amount of heat that must be imparted to one kg of a substance to increase its temperature by 1 Kelvin.

Heat capacity is the ability to absorb some amount of heat during heating or release it during cooling. The heat capacity of a body is the ratio of the infinitesimal amount of heat that the body receives to the corresponding increase in its temperature indicators. The value is measured in J/K. In practice, a slightly different value is used - specific heat capacity.

Definition

What does specific heat capacity mean? This is a quantity related to a unit amount of a substance. Accordingly, the amount of a substance can be measured in cubic meters, kilograms or even moles. What does this depend on? In physics, heat capacity depends directly on what quantitative unit it refers to, and therefore distinguishes between molar, mass and volumetric heat capacity. IN construction industry you won't date molar measurements, but with others - very often.

What affects specific heat capacity?

You know what heat capacity is, but what values ​​affect the indicator is not yet clear. The value of specific heat capacity is directly affected by several components: temperature of the substance, pressure and other thermodynamic characteristics.

As the temperature of a product increases, its specific heat capacity increases, but certain substances have a completely nonlinear curve in this dependence. For example, with an increase in temperature indicators from zero to thirty-seven degrees, the specific heat capacity of water begins to decrease, and if the limit is between thirty-seven and one hundred degrees, then the indicator, on the contrary, will increase.

It is worth noting that the parameter also depends on how the thermodynamic characteristics of the product (pressure, volume, etc.) are allowed to change. For example, the specific heat capacity at stable pressure and at stable volume will be different.

How to calculate the parameter?

Are you interested in what the heat capacity is? The calculation formula is as follows: C=Q/(m·ΔT). What kind of meanings are these? Q is the amount of heat that the product receives when heated (or released by the product during cooling). m is the mass of the product, and ΔT is the difference between the final and initial temperatures of the product. Below is a table of the heat capacity of some materials.

What can be said about calculating heat capacity?

Calculating heat capacity is not the easiest task, especially if you use exclusively thermodynamic methods; it is impossible to do it more precisely. That's why physicists use methods statistical physics or knowledge of the microstructure of products. How to make calculations for gas? The heat capacity of the gas is calculated from the calculation average energy thermal movement of individual molecules in a substance. Molecular movements can be translational or rotational, and inside a molecule there can be a whole atom or vibration of atoms. Classic statistics says that for each degree of freedom of rotational and translational movements is in molar value, which is equal to R/2, and for each vibrational degree of freedom the value is equal to R. This rule is also called the law of equipartition.

In this case, a particle of monatomic gas has only three translational degrees of freedom, and therefore its heat capacity should be equal to 3R/2, which is in excellent agreement with experiment. Each molecule of a diatomic gas is distinguished by three translational, two rotational and one vibrational degrees of freedom, which means that the law of equipartition will be equal to 7R/2, and experience has shown that the heat capacity of a mole of diatomic gas at ordinary temperature is 5R/2. Why was there such a discrepancy between the theories? This is all due to the fact that when establishing heat capacity, it will be necessary to take into account different quantum effects, in other words, use quantum statistics. As you can see, heat capacity is a rather complex concept.

Quantum mechanics says that any system of particles that vibrates or rotates, including a gas molecule, can have certain discrete values energy. If the energy of thermal motion in the installed system is insufficient to excite oscillations of the required frequency, then these oscillations do not contribute to the heat capacity of the system.

In solids, the thermal motion of atoms is weak vibrations near certain equilibrium positions, this applies to nodes crystal lattice. An atom has three vibrational degrees of freedom and, according to the law, the molar heat capacity of a solid body is equal to 3nR, where n is the number of atoms present in the molecule. In practice, this value is the limit to which the heat capacity of a body tends at high temperatures. The value is achieved with normal temperature changes for many elements, this applies to metals, as well as simple compounds. The heat capacity of lead and other substances is also determined.

What about low temperatures?

We already know what heat capacity is, but if we talk about low temperatures, then how will the value be calculated then? If we're talking about about low temperature indicators, then the heat capacity of a solid body then turns out to be proportional T 3 or the so-called Debye's law of heat capacity. Main criterion, allowing to distinguish high performance temperatures from low, it is common to compare them with those characteristic of a certain substance parameter - this can be the characteristic or Debye temperature q D. The presented value is established by the vibration spectrum of atoms in the product and significantly depends on the crystal structure.

In metals, conduction electrons make a certain contribution to the heat capacity. This part heat capacity is calculated using Fermi-Dirac statistics, which takes electrons into account. The electronic heat capacity of a metal, which is proportional to the usual heat capacity, is a relatively small value, and it contributes to the heat capacity of the metal only at temperatures close to absolute zero. Then the lattice heat capacity becomes very small and can be neglected.

Mass heat capacity

Mass specific heat capacity is the amount of heat that is required to be added to a unit mass of a substance in order to heat the product by a unit temperature. Designated given value letter C and it is measured in joules divided by kilogram per kelvin - J/(kg K). That's all for mass heat capacity.

What is volumetric heat capacity?

Volumetric heat capacity is a certain amount of heat that needs to be supplied to a unit volume of a product in order to heat it per unit temperature. Measured this indicator in joules divided by cubic meter per kelvin or J/(m³ K). In many construction reference books, it is the mass specific heat capacity in the work that is considered.

Practical application of heat capacity in the construction industry

Many heat-intensive materials are actively used in the construction of heat-resistant walls. This is extremely important for houses characterized by periodic heating. For example, a stove. Heat-intensive products and walls built from them perfectly accumulate heat, store it during heating periods and gradually release heat after the system is turned off, thus allowing you to maintain an acceptable temperature throughout the day.

So, the more heat stored in the structure, the more comfortable and stable the temperature in the rooms will be.

It is worth noting that ordinary brick and concrete used in house construction have a significantly lower heat capacity than expanded polystyrene. If we take ecowool, it has three times more heat capacity than concrete. It should be noted that it is not for nothing that mass is present in the formula for calculating heat capacity. Thanks to the large, enormous mass of concrete or brick compared to ecowool, it allows the stone walls of structures to accumulate huge amounts of heat and smooth out all daily temperature fluctuations. Only low mass insulation in all frame houses, despite its good heat capacity, is the weakest area of ​​all frame technologies. To decide this problem, impressive heat accumulators are installed in all houses. What is it? These are structural parts that differ large mass with enough good performance heat capacity.

Examples of heat accumulators in real life

What could it be? For example, some internal brick walls, a large stove or fireplace, concrete screeds.

Furniture in any house or apartment is an excellent heat accumulator, because plywood, chipboard and wood can actually store three times more heat per kilogram of weight than the notorious brick.

Are there any disadvantages to thermal accumulators? Of course, the main disadvantage of this approach is that the heat accumulator needs to be designed at the stage of creating a model of a frame house. This is due to the fact that it is heavy, and this will need to be taken into account when creating the foundation, and then imagine how this object will be integrated into the interior. It is worth saying that you will have to take into account not only mass, you will need to evaluate both characteristics in your work: mass and heat capacity. For example, if you use gold with an incredible weight of twenty tons per cubic meter as a heat accumulator, then the product will function as required only twenty-three percent better than a concrete cube that weighs two and a half tons.

Which substance is most suitable for a heat accumulator?

The best product for a heat accumulator it is not concrete and brick at all! Copper, bronze and iron cope well with this task, but they are very heavy. Oddly enough, but the best heat accumulator is water! The liquid has an impressive heat capacity, the largest among substances available to us. More heat capacity only for helium gases (5190 J/(kg K) and hydrogen (14300 J/(kg K), but they are problematic to use in practice. If desired and necessary, see the table of the heat capacity of the substances you need.

The heat capacity of a body is characterized by the amount of heat , necessary to heat this body by one degree (J/deg). If to increase the temperature of a body by T degrees it is necessary to inform it ΔQ joules, then the average heat capacity of the body in the interval ΔT is determined as:

The heat capacity of a body is proportional to its mass and depends on the substance of the body. Specific heat capacity Csp of a given substance (wood, iron, air, etc.) is characterized by the amount of heat per degree, and is measured in J/kg deg. Specific heat.

For gases, it is convenient to use the molar heat capacity (C mole or simply C), characterized by the amount of heat required to heat one kilomole of a given substance by one degree.

It's obvious that

C beat /J/kg * deg/ * μ/kg/kmol/ = C /J/kmol * deg/.

Since 1 kilomole of any gas contains the same number of molecules, and the average kinetic energy of molecules does not depend on their mass, we can expect that the molar heat capacities of all sufficiently rarefied gases should be the same.

The heat capacity of a body depends significantly on how the states of the body change during the heating process. For simplicity, let us consider an ideal monatomic gas. If we heat a gas enclosed in a closed volume, V = const (Fig. 1, a), then all the supplied heat ΔQ will only go to increase the internal energy of the gas. Then the first law of thermodynamics at ΔA = 0 will have the form: ΔQ = ΔU.

In this case, the temperature of the gas will increase in accordance with the increase in its internal energy, which means that the temperature of an ideal gas is proportional to its internal energy. The gas pressure R. will also increase in proportion to the temperature. Let us denote the heat capacity of a gas at constant volume by C.

If we want pressure to be maintained during the heating process, the gas must be allowed to expand. To do this, we place the gas in a cylinder with a piston, which is subject to constant pressure P = const (Fig. 1, b). Since the internal energy U of an ideal gas does not depend on its volume, the amount of heat required to increase it will remain the same. But when the gas is heated to the same temperature, part of the supplied heat is now spent on work against external forces during the expansion of the gas. Consequently, to heat the gas to the same temperature as in the previous case (V = const), more heat will have to be expended. Thus, the heat capacity ΔQ/ΔT of gas at constant pressure, which we denote by C p. , will be greater than C V .

This example is very important. It shows that the amount of heat ΔQ required to heat the gas by ΔT degrees depends significantly on additional conditions - the nature of measurements of other microscopic parameters that determine the state of the gas, i.e. P. and V. In addition to the considered processes characterized by the simplest additional conditions V = const and P. = const, we can consider many others that correspond various changes V and R. when heated. Each process will have its own heat capacity C.

Values ​​C r. and C v for an ideal gas are related by a simple relation:

From r. – С v = R (2)

This relationship is called Robert Mayer's law, which he obtained in 1842.

For an ideal gas, the molar heat capacity at constant pressure exceeds the molar heat capacity at constant volume by the value R, i.e., by 8.31 kJ/kmol deg.

The universal gas constant R is numerically equal to the work of expansion of a kilomole of an ideal gas when it is heated by one degree at constant pressure.

Experience shows that in all cases the conversion of mechanical energy into thermal energy and vice versa always occurs in strictly equivalent quantities. Since thermal motion is ultimately also mechanical movement individual molecules (only not directed, but chaotic), then during all these transformations the law of conservation of energy must be observed, taking into account the energy of not only external, but also internal movements. This general formulation of this law is called the first law of thermodynamics and is written as:

ΔQ = ΔU + ΔA, i.e.

The amount of heat imparted to the body (ΔQ) goes to increase internal energy (ΔU) and to perform work with heat (ΔA).

However, if the vessel with the expanding gas is thermally insulated from the environment, then there will be no heat exchange, i.e. ΔQ = 0. The process occurring under this condition is called adiabatic. The equation of the first law of thermodynamics for an adiabatic process will then take the form:

ΔQ = 0 0 = ΔU + ΔA or ΔA = - ΔU. (3)

Consequently, during an adiabatic process, work is done only due to the internal energy of the gas. During adiabatic expansion, the gas does work, and its internal energy and, therefore, temperature drop. During adiabatic compression, the gas work is negative ( external environment performs work on the gas), the internal energy and temperature of the gas increase.

The heat capacity during an adiabatic process will be equal to 0, i.e.

The equation describing the adiabatic process has the form:

PV γ = const; where γ = С Р /С V. (4)

Since С Р >С V, then γ>1 and the curve depicted by equation (4) is steeper than the isotherm (Fig. 2). The amount of work done by an adiabatic process can be especially easily calculated using equation (3):

For a monatomic gas C = 12.5 kJ/k mol deg, C r. =C v + =20.8 kJ/k mol deg and the adiabatic exponent γ=C P /C v =1.67.

For diatomic gases at ordinary temperatures

g=29.1/20.8=1.4.

For polyatomic gases, γ is even closer to unity.

In high-speed engines internal combustion and when gases flow through the nozzles jet engines the gas expansion process proceeds so quickly that it can be considered practically adiabatic and

calculate using equation /4/.

Experience also shows that for sound vibrations with minimum frequencies, during one oscillation /~0.1 s/the temperature between the compressed/ and thereby heated/ and discharged / and thus cooled/ regions of the wave does not have time to level out. In practice, the process of sound propagation can be considered adiabatic, so the speed of sound propagation in ideal gas is determined by the expression:

It's easy to find from here:

Thus, the determination of γ comes down to measuring the speed of sound and absolute temperature air. In this work, the speed of sound is determined by the standing wave method - the Kundt method.

II. DESCRIPTION OF THE EXPERIMENTAL INSTALLATION.

Scheme experimental setup is shown in Figure 3. Telephone T, receiving an electrical signal from generator 1, emits sound waves into pipe 2. Having reached microphone M, the sound wave is converted into voltage, which is supplied to the vertical deflection plates of the electronic oscilloscope 3. Voltage is supplied directly to the horizontal deflection plates X from the output terminals of the sound generator. The phone is rigidly fixed to the left end of the tube, and the microphone can move freely inside it.

The phase shift of the signal arriving at the Y plates relative to the signal supplied to the X plates depends on the time it takes the sound to travel the distance between the microphone and the telephone, and can be used to determine the wavelength λ. When you turn on the installation, the Ellis should be visible on the oscilloscope screen. By changing the distance between the microphone and the phone, you can turn the ellipse into a straight line. If we now move the microphone by λ/2, a straight line will again appear on the screen, this time passing through other quadrants. With further displacement, the straight line will again change its direction, etc. Thus, using figures called Lissajous figures, you can directly measure the length sound wave in the air and use the formula to determine the speed of sound, where is the frequency of the generator in Hz.

III. PROCEDURE FOR CARRYING OUT MEASUREMENTS.

1. Turn on the oscilloscope and allow it to warm up for 10 minutes.

2. Turn on and tune the sound generator to the frequency /frequency set by the teacher/. Set the voltage at the generator output to 1.5 V.

3. Set the microphone rod indicator 5 to the extreme right position of scale 4 /Fig/, and a Lissajous figure /ellipse or straight line/ will appear on the oscilloscope screen.

4. Moving the rod with the microphone to the left, fix the position of the microphone rod / /, at which the ellipse turns into a clear straight line, which corresponds to the nodes standing wave/count in cm on a scale of 4/.

5. Calculate the difference between the nodal points, which is half the wavelength.

11.Draw conclusions.

IV. TEST QUESTIONS.

See work No. 10.