Heat capacity is the ability to absorb some amount of heat during heating or give it away when cooled. The heat capacity of a body is the ratio of an infinitesimal amount of heat that a 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 single amount of a substance. Accordingly, the amount of a substance can be measured in cubic meters, kilograms, or even in moles. What does it depend on? In physics, the heat capacity depends directly on which quantitative unit it refers to, which means that they distinguish between molar, mass and volumetric heat capacity. In the construction industry, you will not meet with molar measurements, but with others - all the time.

What affects specific heat capacity?

You know what heat capacity is, but what values ​​\u200b\u200baffect the indicator is not yet clear. The value of specific heat is directly affected by several components: the temperature of the substance, pressure and other thermodynamic characteristics.

As the temperature of the product rises, its specific heat capacity increases, however, certain substances differ in a completely non-linear 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, and so on) are allowed to change. For example, the specific heat at a stable pressure and at a stable volume will be different.

How to calculate the parameter?

Are you interested in what is the heat capacity? The calculation formula is as follows: C \u003d Q / (m ΔT). What are these values? 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 the calculation of heat capacity?

Calculating the heat capacity is not an easy task, especially if only thermodynamic methods are used, it is impossible to do it more precisely. Therefore, physicists use the methods of statistical physics or knowledge of the microstructure of products. How to calculate for gas? The heat capacity of a gas is calculated from the calculation of the average energy of thermal motion of individual molecules in a substance. The movements of molecules can be of a translational and rotational type, and inside a molecule there can be a whole atom or vibration of atoms. Classical statistics says that for each degree of freedom of rotational and translational movements, there is a 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 equipartition law.

In this case, a particle of a monatomic gas differs by 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 diatomic gas molecule has three translational, two rotational and one vibrational degrees of freedom, which means that the equipartition law will be 7R/2, and experience has shown that the heat capacity of a mole of a diatomic gas at ordinary temperature is 5R/2. Why was there such a discrepancy in theory? Everything is due to the fact that when establishing the heat capacity, it will be necessary to take into account various quantum effects, in other words, to use quantum statistics. As you can see, heat capacity is a rather complicated concept.

Quantum mechanics says that any system of particles that oscillate or rotate, including a gas molecule, can have certain discrete energy values. 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 a weak oscillation around certain equilibrium positions, this applies to the nodes of the 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 the body tends at high temperatures. The value is achieved with normal temperature changes in many elements, this applies to metals, as well as simple compounds. The heat capacity of lead and other substances is also determined.

What can be said about low temperatures?

We already know what heat capacity is, but if we talk about low temperatures, how will the value be calculated then? If we are talking 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. The main criterion for distinguishing high temperatures from low ones is the usual comparison of them with a parameter characteristic of a particular substance - this can be the characteristic or Debye temperature q D . The presented value is set by the vibration spectrum of atoms in the product and depends significantly on the crystal structure.

In metals, conduction electrons make a certain contribution to the heat capacity. This part of the heat capacity is calculated using the 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 brought to a unit mass of a substance in order to heat the product per unit temperature. This value is denoted by the letter C and it is measured in joules divided by a kilogram per kelvin - J / (kg K). This is all that concerns the heat capacity of the mass.

What is volumetric heat capacity?

Volumetric heat capacity is a certain amount of heat that needs to be brought to a unit volume of production in order to heat it per unit temperature. This indicator is measured in joules divided by a cubic meter per kelvin or J / (m³ K). In many building reference books, it is the mass specific heat capacity in 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 that are characterized by periodic heating. For example, oven. Heat-intensive products and walls built from them perfectly accumulate heat, store it during heating periods of time 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 is stored in the structure, the more comfortable and stable the temperature in the rooms will be.

It should be noted that ordinary brick and concrete used in housing construction have a significantly lower heat capacity than expanded polystyrene. If we take ecowool, then it is three times more heat-consuming than concrete. It should be noted that in the formula for calculating the heat capacity, it is not in vain that there is mass. Due to the large huge mass of concrete or brick, in comparison with ecowool, it allows accumulating huge amounts of heat in the stone walls of structures and smoothing out all daily temperature fluctuations. Only a small mass of insulation in all frame houses, despite the good heat capacity, is the weakest area for all frame technologies. To solve this problem, impressive heat accumulators are installed in all houses. What it is? These are structural parts that are characterized by a large mass with a fairly good heat capacity index.

Examples of heat accumulators in 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 heat only per kilogram of weight three times more than the notorious brick.

Are there any drawbacks to thermal storage? Of course, the main disadvantage of this approach is that the heat accumulator needs to be designed at the stage of creating a frame house layout. All due to the fact that it is very 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 it is necessary to take into account not only the mass, it will be necessary to evaluate both characteristics in the work: mass and heat capacity. For example, if you use gold with an incredible weight of twenty tons per cubic meter as a heat storage, then the product will function as it should only twenty-three percent better than a concrete cube, which weighs two and a half tons.

Which substance is most suitable for a heat storage?

The best product for a heat accumulator is not concrete and brick at all! Copper, bronze and iron do a good job of this, but they are very heavy. Oddly enough, but the best heat accumulator is water! The liquid has an impressive heat capacity, the largest among the substances available to us. Only helium gases (5190 J / (kg K) and hydrogen (14300 J / (kg K)) have more heat capacity, but they are problematic to apply in practice. If you wish and need, see the heat capacity table of the substances you need.

Let us now introduce a very important thermodynamic characteristic called heat capacity systems(traditionally denoted by the letter With with different indices).

Heat capacity - value additive, it depends on the amount of substance in the system. Therefore, we also introduce specific heat

Specific heat is the heat capacity per unit mass of a substance

and molar heat capacity

Molar heat capacity is the heat capacity of one mole of a substance

Since the amount of heat is not a state function and depends on the process, the heat capacity will also depend on the way heat is supplied to the system. To understand this, let us recall the first law of thermodynamics. Dividing the equality ( 2.4) per elementary increment of absolute temperature dT, we get the relation

The second term, as we have seen, depends on the type of process. We note that in the general case of a nonideal system, the interaction of whose particles (molecules, atoms, ions, etc.) cannot be neglected (see, for example, § 2.5 below, in which the van der Waals gas is considered), the internal energy depends not only on temperature, but also on the volume of the system. This is explained by the fact that the interaction energy depends on the distance between the interacting particles. When the volume of the system changes, the concentration of particles changes, respectively, the average distance between them changes and, as a result, the interaction energy and the entire internal energy of the system change. In other words, in the general case of a nonideal system

Therefore, in the general case, the first term cannot be written as a total derivative, the total derivative must be replaced by a partial derivative with an additional indication of the constant value at which it is calculated. For example, for an isochoric process:

.

Or for an isobaric process

The partial derivative included in this expression is calculated using the equation of state of the system, written as . For example, in the particular case of an ideal gas

this derivative is

.

We will consider two special cases corresponding to the heat supply process:

• constant volume;
• constant pressure in the system.

In the first case, work dА = 0 and we get the heat capacity C V ideal gas at constant volume:

Taking into account the reservation made above, for a nonideal system relation (2.19) must be written in the following general form

Replacing in 2.7 on , and on , we immediately get:

.

To calculate the heat capacity of an ideal gas With p at constant pressure ( dp=0) we take into account that from the equation ( 2.8) follows the expression for elementary work with an infinitesimal change in temperature

We get in the end

Dividing this equation by the number of moles of a substance in the system, we obtain a similar relationship for molar heat capacities at constant volume and pressure, called Mayer's ratio

For reference, we give a general formula - for an arbitrary system - connecting the isochoric and isobaric heat capacities:

Expressions (2.20) and (2.21) are obtained from this formula by substituting into it the expression for the internal energy of an ideal gas and using his equation of state (see above):

.

The heat capacity of a given mass of matter at constant pressure is greater than the heat capacity at constant volume, since part of the input energy is spent on doing work and for the same heating, more heat is required. Note that from (2.21) follows the physical meaning of the gas constant:

Thus, the heat capacity turns out to depend not only on the type of substance, but also on the conditions under which the process of temperature change occurs.

As we can see, the isochoric and isobaric heat capacities of an ideal gas do not depend on the gas temperature; for real substances, these heat capacities depend, generally speaking, also on the temperature itself. T.

The isochoric and isobaric heat capacities of an ideal gas can also be obtained directly from the general definition, using the formulas obtained above ( 2.7) and (2.10 ) for the amount of heat obtained by an ideal gas in these processes.

For an isochoric process, the expression for C V follows from ( 2.7):

For an isobaric process, the expression for C p follows from (2.10):

For molar heat capacities hence the following expressions are obtained

The ratio of heat capacities is equal to the adiabatic index:

At the thermodynamic level, it is impossible to predict the numerical value g; we managed to do this only when considering the microscopic properties of the system (see expression (1.19 ), as well as ( 1.28) for a mixture of gases). From formulas (1.19) and (2.24), theoretical predictions follow for the molar heat capacities of gases and the adiabatic exponent.

Monatomic gases (i = 3):

Diatomic gases (i = 5):

Polyatomic gases (i = 6):

Experimental data for various substances are shown in Table 1.

Table 1

Substance			g

It can be seen that the simple model of ideal gases generally describes the properties of real gases quite well. Note that the agreement was obtained without taking into account the vibrational degrees of freedom of the gas molecules.

We have also given the values ​​of the molar heat capacity of some metals at room temperature. If we imagine the crystal lattice of a metal as an ordered set of solid balls connected by springs to neighboring balls, then each particle can only oscillate in three directions ( i count = 3), and each such degree of freedom is associated with a kinetic k V T/2 and the same potential energy. Therefore, a crystal particle has an internal (oscillatory) energy k V T. Multiplying by the Avogadro number, we get the internal energy of one mole

where does the value of the molar heat capacity come from

(Due to the small coefficient of thermal expansion of solids, they do not distinguish with p and c v). The above relation for the molar heat capacity of solids is called the law of Dulong and Petit, and the table shows a good match of the calculated value

with experiment.

Speaking about the good agreement between the above ratios and experimental data, it should be noted that it is observed only in a certain temperature range. In other words, the heat capacity of the system depends on the temperature, and formulas (2.24) have a limited scope. Consider first Fig. 2.10, which shows the experimental dependence of the heat capacity with TV hydrogen gas from absolute temperature T.

Rice. 2.10. Molar heat capacity of gaseous hydrogen Н2 at constant volume as a function of temperature (experimental data)

Below, for brevity, we talk about the absence of certain degrees of freedom in molecules in certain temperature ranges. Once again, we recall that we are actually talking about the following. For quantum reasons, the relative contribution to the internal energy of the gas of individual types of motion really depends on the temperature and in certain temperature intervals can be so small that in the experiment - always performed with finite accuracy - it is not noticeable. The result of the experiment looks as if these types of motion do not exist, and there are no corresponding degrees of freedom. The number and nature of the degrees of freedom are determined by the structure of the molecule and the three-dimensionality of our space - they cannot depend on temperature.

The contribution to internal energy depends on temperature and can be small.

At temperatures below 100 K heat capacity

which indicates the absence of both rotational and vibrational degrees of freedom in the molecule. Further, with increasing temperature, the heat capacity rapidly increases to the classical value

characteristic of a diatomic molecule with a rigid bond, in which there are no vibrational degrees of freedom. At temperatures above 2000 K the heat capacity discovers a new jump to the value

This result also indicates the appearance of vibrational degrees of freedom. But all this still looks inexplicable. Why can't a molecule rotate at low temperatures? And why do vibrations in a molecule occur only at very high temperatures? In the previous chapter, a brief qualitative discussion of the quantum reasons for this behavior was given. And now we can only repeat that the whole thing comes down to specifically quantum phenomena that cannot be explained from the standpoint of classical physics. These phenomena are discussed in detail in subsequent sections of the course.

Additional Information

http://www.plib.ru/library/book/14222.html - Yavorsky B.M., Detlaf A.A. Handbook of Physics, Science, 1977 - p. 236 - table of characteristic "turn-on" temperatures of vibrational and rotational degrees of freedom of molecules for some specific gases;

Let us now turn to fig. 2.11, representing the dependence of the molar heat capacities of three chemical elements (crystals) on temperature. At high temperatures, all three curves tend to the same value

corresponding to the Dulong and Petit law. Lead (Pb) and iron (Fe) practically have this limiting heat capacity already at room temperature.

Rice. 2.11. The dependence of the molar heat capacity for three chemical elements - crystals of lead, iron and carbon (diamond) - on temperature

For diamond (C), this temperature is not yet high enough. And at low temperatures, all three curves show a significant deviation from the Dulong and Petit law. This is another manifestation of the quantum properties of matter. Classical physics turns out to be powerless to explain many regularities observed at low temperatures.

Additional Information

http://eqworld.ipmnet.ru/ru/library/physics/thermodynamics.htm - J. de Boer Introduction to molecular physics and thermodynamics, Ed. IL, 1962 - pp. 106–107, part I, § 12 - the contribution of electrons to the heat capacity of metals at temperatures close to absolute zero;

http://ilib.mirror1.mccme.ru/djvu/bib-kvant/kvant_82.htm - Perelman Ya.I. Do you know physics? Library "Quantum", issue 82, Science, 1992. Page 132, question 137: which bodies have the highest heat capacity (see the answer on p. 151);

http://ilib.mirror1.mccme.ru/djvu/bib-kvant/kvant_82.htm - Perelman Ya.I. Do you know physics? Library "Quantum", issue 82, Science, 1992. Page 132, question 135: about heating water in three states - solid, liquid and vapor (see the answer on p. 151);

http://www.femto.com.ua/articles/part_1/1478.html - physical encyclopedia. Calorimetry. Methods for measuring heat capacities are described.

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 a given process. The change in the internal energy of a body during heat transfer is characterized by a quantity called the amount of heat.

is the change in the internal energy of the body in the process of heat transfer without doing work. The amount of heat is denoted by the letter Q .

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

In thermal measurements, a special unit of energy, the calorie ( feces), equal to the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius (more precisely, from 19.5 to 20.5 ° C). This unit, in particular, is currently used in calculating the consumption of heat (thermal energy) in apartment buildings. Empirically, the mechanical equivalent of heat has been established - the ratio between calories and joules: 1 cal = 4.2 J.

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

If you pour 100 g of water into two identical vessels, and 400 g into another at the same temperature and put them on the same burners, then the water in the first vessel will boil earlier. Thus, the greater the mass of the body, the greater the amount of heat it needs to heat up. The same goes for cooling.

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

- this is a physical quantity equal to the amount of heat that must be reported to 1 kg of a substance to heat it by 1 ° C (or 1 K). The same amount of heat is given off by 1 kg of a substance when cooled by 1 °C.

The specific heat capacity is denoted by the letter with. The unit of specific heat capacity is 1 J/kg °C or 1 J/kg °K.

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

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 1 °C. In particular, the internal energy of 1 kg of lead, when it is heated by 1 °C, increases by 140 J, and when it is cooled, it decreases by 140 J.

Q required to heat the body mass m temperature t 1 °С up to temperature t 2 °С, is equal to the product of the specific heat capacity of the substance, body mass and the difference between the final and initial temperatures, i.e.

Q \u003d c ∙ m (t 2 - t 1)

According to the same formula, the amount of heat that the body gives off when cooled is also calculated. Only in this case should the final temperature be subtracted from the initial temperature, i.e. Subtract the smaller temperature from the larger temperature.

This is a synopsis on the topic. "Quantity of heat. Specific heat". Choose next steps:

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Water is one of the most amazing substances. Despite its wide distribution and widespread use, it is a real mystery of nature. Being one of the oxygen compounds, it would seem that water should have very low characteristics such as freezing, heat of vaporization, etc. But this does not happen. The heat capacity of water alone, in spite of everything, is extremely high.

Water is able to absorb a huge amount of heat, while itself practically not heating up - this is its physical feature. water is about five times higher than the heat capacity of sand, and ten times higher than iron. Therefore, water is a natural coolant. Its ability to accumulate a large amount of energy makes it possible to smooth out temperature fluctuations on the Earth's surface and regulate the thermal regime throughout the planet, and this happens regardless of the time of year.

This unique property of water makes it possible to use it as a coolant in industry and at home. In addition, water is a widely available and relatively cheap raw material.

What is meant by heat capacity? As is known from the course of thermodynamics, heat transfer always occurs from a hot to a cold body. In this case, we are talking about the transition of a certain amount of heat, and the temperature of both bodies, being a characteristic of their state, shows the direction of this exchange. In the process of a metal body with water of equal mass at the same initial temperatures, the metal changes its temperature several times more than water.

If we take as a postulate the main statement of thermodynamics - from two bodies (isolated from others), during heat exchange, one gives off and the other receives an equal amount of heat, then it becomes clear that metal and water have completely different heat capacities.

Thus, the heat capacity of water (as well as any substance) is an indicator that characterizes the ability of a given substance to give (or receive) some during cooling (heating) per unit temperature.

The specific heat capacity of a substance is the amount of heat required to heat a unit of this substance (1 kilogram) by 1 degree.

The amount of heat released or absorbed by a body is equal to the product of specific heat capacity, mass and temperature difference. It is measured in calories. One calorie is exactly the amount of heat that is enough to heat 1 g of water by 1 degree. For comparison: the specific heat capacity of air is 0.24 cal/g ∙°C, aluminum is 0.22, iron is 0.11, and mercury is 0.03.

The heat capacity of water is not a constant. With an increase in temperature from 0 to 40 degrees, it slightly decreases (from 1.0074 to 0.9980), while for all other substances this characteristic increases during heating. In addition, it can decrease with increasing pressure (at depth).

As you know, water has three states of aggregation - liquid, solid (ice) and gaseous (steam). At the same time, the specific heat capacity of ice is approximately 2 times lower than that of water. This is the main difference between water and other substances, the specific heat capacity of which in the solid and molten state does not change. What is the secret here?

The fact is that ice has a crystalline structure, which does not immediately collapse when heated. Water contains small particles of ice, which consist of several molecules and are called associates. When water is heated, a part is spent on the destruction of hydrogen bonds in these formations. This explains the unusually high heat capacity of water. The bonds between its molecules are completely destroyed only when water passes into steam.

The specific heat capacity at a temperature of 100°C almost does not differ from that of ice at 0°C. This once again confirms the correctness of this explanation. The heat capacity of steam, like the heat capacity of ice, is now much better understood than that of water, on which scientists have not yet come to a consensus.

Specific heat capacity is a characteristic of a substance. That is, it is different for different substances. In addition, the same substance, but in different states of aggregation, has different specific heat capacities. Thus, it is correct to speak of the specific heat of a substance (the specific heat of water, the specific heat of gold, the specific heat of wood, etc.).

The specific heat capacity of a particular substance shows how much heat (Q) must be transferred to it in order to heat 1 kilogram of this substance by 1 degree Celsius. Specific heat capacity is denoted by the Latin letter c. That is, c = Q/mt. Considering that t and m are equal to one (1 kg and 1 °C), then the specific heat capacity is numerically equal to the amount of heat.

However, heat and specific heat have different units. Heat (Q) in the C system is measured in Joules (J). And the specific heat capacity is in Joules divided by a kilogram multiplied by a degree Celsius: J / (kg ° C).

If the specific heat capacity of a substance is, for example, 390 J/(kg °C), then this means that if 1 kg of this substance is heated by 1 °C, then it will absorb 390 J of heat. Or, in other words, in order to heat 1 kg of this substance by 1 °C, 390 J of heat must be transferred to it. Or, if 1 kg of this substance is cooled by 1 ° C, then it will give off 390 J of heat.

If, however, not 1, but 2 kg of a substance is heated by 1 ° C, then twice as much heat must be transferred to it. So for the example above, it will already be 780 J. The same will happen if 1 kg of a substance is heated by 2 ° C.

The specific heat capacity of a substance does not depend on its initial temperature. That is, if, for example, liquid water has a specific heat capacity of 4200 J / (kg ° C), then heating at least twenty-degree or ninety-degree water by 1 ° C will equally require 4200 J of heat per 1 kg.

But ice has a specific heat capacity different from liquid water, almost two times less. However, in order to heat it by 1 °C, the same amount of heat per 1 kg is required, regardless of its initial temperature.

The specific heat capacity also does not depend on the shape of the body, which is made of a given substance. A steel bar and a steel sheet, having the same mass, will require the same amount of heat to heat them by the same number of degrees. Another thing is that in this case the exchange of heat with the environment should be neglected. The sheet has a larger surface than the bar, which means that the sheet gives off more heat, and therefore it will cool faster. But under ideal conditions (when heat loss can be neglected), the shape of the body does not play a role. Therefore, they say that specific heat is a characteristic of a substance, but not of a body.

So, the specific heat capacity of different substances is different. This means that if different substances of the same mass and with the same temperature are given, then in order to heat them to a different temperature, they need to transfer a different amount of heat. For example, a kilogram of copper will require about 10 times less heat than water. That is, the specific heat capacity of copper is about 10 times less than that of water. We can say that "less heat is placed in copper."

The amount of heat that must be transferred to the body in order to heat it from one temperature to another is found by the following formula:

Q \u003d cm (t to - t n)

Here t to and t n are the final and initial temperatures, m is the mass of the substance, c is its specific heat. Specific heat capacity is usually taken from tables. From this formula, the specific heat capacity can be expressed.