Calculation of the amount of heat required to heat a body or released by it during cooling. Quantity of heat. Specific heat

1. 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 internal energy of a body during heat transfer is characterized by a quantity called amount of heat.

The amount of heat is the change in the internal energy of a body during the process of heat transfer without doing work.

The amount of heat is denoted by the letter $Q$ . Since the amount of heat is a measure of the change in internal energy, its unit is the joule (1 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.

2. 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, the greater the mass of a body, the greater the amount of heat it requires to heat up. The same is true with cooling: when a body of greater mass is cooled, it gives off a greater amount of heat. These bodies are made of the same substance and they heat up or cool down by the same number of degrees.

3. If we now heat 100 g of water from 30 to 60 °C, i.e. at 30 °C, and then up to 100 °C, i.e. by 70 °C, then in the first case it will take less time to heat up than in the second, and, accordingly, heating water by 30 °C will require less heat than heating water by 70 °C. Thus, the amount of heat is directly proportional to the difference between the final $(t_2\,^\circ C) $ and initial $(t_1\,^\circ C) $ temperatures: $Q\sim(t_2- t_1) $ .

4. If you now pour 100 g of water into one vessel, and pour a little water into another identical vessel and put in it a metal body such that its mass and the mass of water are 100 g, and heat the vessels on identical tiles, then you will notice that in a vessel containing only water will have a lower temperature than one containing water and a metal body. Therefore, in order for the temperature of the contents in both vessels to be the same, it is necessary to transfer more heat to the water than to the water and the metal body. Thus, the amount of heat required to heat a body depends on the type of substance from which the body is made.

5. The 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 of a substance.

A 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) is called the specific heat capacity of the substance.

1 kg of substance releases the same amount of heat when cooled by 1 °C.

Specific heat capacity is denoted by the letter $c$ . 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.

The specific heat of lead is 140 J/kg °C. This means that to heat 1 kg of lead by 1 °C it is necessary to expend an amount of heat of 140 J. The same amount of heat will be released when 1 kg of water cools by 1 °C.

Since the amount of heat is equal to the change in the internal energy of the body, we can say that specific heat capacity shows how much the internal energy of 1 kg of a substance changes 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.

The amount of heat $Q $ required to heat a body of mass $m $ from temperature $(t_1\,^\circ C) $ to temperature $(t_2\,^\circ C) $ 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.

\[ Q=cm(t_2()^\circ-t_1()^\circ) \]

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. Subtract the smaller temperature from the larger temperature.

6. Example of problem solution. 100 g of water at a temperature of 20 °C is poured into a glass containing 200 g of water at a temperature of 80 °C. After which the temperature in the vessel reached 60 °C. How much heat did the cold water receive and how much heat did the hot water give out?

When solving a problem, you must perform the following sequence of actions:

write down briefly the conditions of the problem;
convert the values of quantities to SI;
analyze the problem, establish which bodies are involved in heat exchange, which bodies give off energy and which receive;
solve the problem in general form;
perform calculations;
analyze the received answer.

1. The task.

Given:
$m_1 $ = 200 g
$m_2$ = 100 g
$t_1 $ = 80 °C
$t_2 $ = 20 °C
$t$ = 60 °C
______________

$Q_1 $ — ? $Q_2 $ — ?
$c_1 $ = 4200 J/kg °C

2. SI:$m_1$ = 0.2 kg; $m_2$ = 0.1 kg.

3. Task analysis. The problem describes the process of heat exchange between hot and cold water. Hot water gives off an amount of heat $Q_1 $ and cools from temperature $t_1 $ to temperature $t $ . Cold water receives the amount of heat $Q_2 $ and is heated from temperature $t_2 $ to temperature $t $ .

4. Solution of the problem in general form. The amount of heat given off by hot water is calculated by the formula: $Q_1=c_1m_1(t_1-t) $ .

The amount of heat received by cold water is calculated by the formula: $Q_2=c_2m_2(t-t_2) $ .

5. Computations.
$Q_1 $ = 4200 J/kg · °С · 0.2 kg · 20 °С = 16800 J
$Q_2$ = 4200 J/kg °C 0.1 kg 40 °C = 16800 J

6. The answer is that the amount of heat given off by hot water is equal to the amount of heat received by cold water. In this case, an idealized situation was considered and it was not taken into account that a certain amount of heat was used to heat the glass in which the water was located and the surrounding air. In reality, the amount of heat given off by hot water is greater than the amount of heat received by cold water.

Part 1

1. The specific heat capacity of silver is 250 J/(kg °C). What does this mean?

1) when 1 kg of silver cools at 250 °C, an amount of heat of 1 J is released
2) when 250 kg of silver cools by 1 °C, an amount of heat of 1 J is released
3) when 250 kg of silver cools by 1 °C, an amount of heat of 1 J is absorbed
4) when 1 kg of silver cools by 1 °C, an amount of heat of 250 J is released

2. The specific heat capacity of zinc is 400 J/(kg °C). It means that

1) when 1 kg of zinc is heated by 400 °C, its internal energy increases by 1 J
2) when 400 kg of zinc is heated by 1 °C, its internal energy increases by 1 J
3) to heat 400 kg of zinc by 1 °C it is necessary to expend 1 J of energy
4) when 1 kg of zinc is heated by 1 °C, its internal energy increases by 400 J

3. When transferring the amount of heat $Q $ to a solid body with mass $m $ , the body temperature increased by $\Delta t^\circ $ . Which of the following expressions determines the specific heat capacity of the substance of this body?

1) $\frac(m\Delta t^\circ)(Q) $
2) $\frac(Q)(m\Delta t^\circ) $
3) $\frac(Q)(\Delta t^\circ) $
4) $Qm\Delta t^\circ $

4. The figure shows a graph of the dependence of the amount of heat required to heat two bodies (1 and 2) of the same mass on temperature. Compare the specific heat capacity values ($c_1 $ and $c_2 $ ) of the substances from which these bodies are made.

1) $c_1=c_2 $
2) $c_1>c_2 $
3)\(c_1 4) the answer depends on the value of the mass of the bodies

5. The diagram shows the amount of heat transferred to two bodies of equal mass when their temperature changes by the same number of degrees. Which relationship is correct for the specific heat capacities of the substances from which bodies are made?

1) $c_1=c_2$
2) $c_1=3c_2$
3) $c_2=3c_1$
4) $c_2=2c_1$

6. The figure shows a graph of the temperature of a solid body depending on the amount of heat it gives off. Body weight 4 kg. What is the specific heat capacity of the substance of this body?

1) 500 J/(kg °C)
2) 250 J/(kg °C)
3) 125 J/(kg °C)
4) 100 J/(kg °C)

7. When heating a crystalline substance weighing 100 g, the temperature of the substance and the amount of heat imparted to the substance were measured. The measurement data was presented in table form. Assuming that energy losses can be neglected, determine the specific heat capacity of the substance in the solid state.

1) 192 J/(kg °C)
2) 240 J/(kg °C)
3) 576 J/(kg °C)
4) 480 J/(kg °C)

8. To heat 192 g of molybdenum by 1 K, you need to transfer an amount of heat of 48 J to it. What is the specific heat of this substance?

1) 250 J/(kg K)
2) 24 J/(kg K)
3) 4·10 -3 J/(kg K)
4) 0.92 J/(kg K)

9. What amount of heat is needed to heat 100 g of lead from 27 to 47 °C?

1) 390 J
2) 26 kJ
3) 260 J
4) 390 kJ

10. Heating a brick from 20 to 85 °C requires the same amount of heat as heating water of the same mass by 13 °C. The specific heat capacity of the brick is

1) 840 J/(kg K)
2) 21000 J/(kg K)
3) 2100 J/(kg K)
4) 1680 J/(kg K)

11. From the list of statements below, select two correct ones and write their numbers in the table.

1) The amount of heat that a body receives when its temperature increases by a certain number of degrees is equal to the amount of heat that this body gives off when its temperature decreases by the same number of degrees.
2) When a substance cools, its internal energy increases.
3) The amount of heat that a substance receives when heated is used mainly to increase the kinetic energy of its molecules.
4) The amount of heat that a substance receives when heated is used mainly to increase the potential energy of interaction of its molecules
5) The internal energy of a body can be changed only by imparting a certain amount of heat to it

12. The table presents the results of measurements of mass $m$ , temperature changes $\Delta t$ and the amount of heat $Q$ released during cooling of cylinders made of copper or aluminum.

Which statements correspond to the results of the experiment? Select two correct ones from the list provided. Indicate their numbers. Based on the measurements taken, it can be argued that the amount of heat released during cooling

1) depends on the substance from which the cylinder is made.
2) does not depend on the substance from which the cylinder is made.
3) increases with increasing cylinder mass.
4) increases with increasing temperature difference.
5) the specific heat capacity of aluminum is 4 times greater than the specific heat capacity of tin.

Part 2

C1. A solid body weighing 2 kg is placed in a 2 kW furnace and begins to heat up. The figure shows the dependence of the temperature $t$ of this body on the heating time $\tau $ . What is the specific heat capacity of the substance?

1) 400 J/(kg °C)
2) 200 J/(kg °C)
3) 40 J/(kg °C)
4) 20 J/(kg °C)

Answers

(or heat transfer).

Specific heat capacity of a substance.

Heat capacity- this is the amount of heat absorbed by a body when heated by 1 degree.

The heat capacity of a body is indicated by a capital Latin letter WITH.

What does the heat capacity of a body depend on? First of all, from its mass. It is clear that heating, for example, 1 kilogram of water will require more heat than heating 200 grams.

What about the type of substance? Let's do an experiment. Let's take two identical vessels and, having poured water weighing 400 g into one of them, and vegetable oil weighing 400 g into the other, we will begin to heat them using identical burners. By observing the thermometer readings, we will see that the oil heats up quickly. To heat water and oil to the same temperature, the water must be heated longer. But the longer we heat the water, the more heat it receives from the burner.

Thus, heating the same mass of different substances to the same temperature requires different amounts of heat. The amount of heat required to heat a body and, therefore, its heat capacity depend on the type of substance of which the body is composed.

So, for example, to increase the temperature of water weighing 1 kg by 1°C, an amount of heat equal to 4200 J is required, and to heat the same mass of sunflower oil by 1°C, an amount of heat equal to 1700 J is required.

A physical quantity showing how much heat is required to heat 1 kg of a substance by 1 ºС is called specific heat capacity of this substance.

Each substance has its own specific heat capacity, which is denoted by the Latin letter c and measured in joules per kilogram degree (J/(kg °C)).

The specific heat capacity of the same substance in different states of aggregation (solid, liquid and gaseous) is different. For example, the specific heat capacity of water is 4200 J/(kg °C), and the specific heat capacity of ice is 2100 J/(kg °C); aluminum in the solid state has a specific heat capacity of 920 J/(kg - °C), and in the liquid state - 1080 J/(kg - °C).

Note that water has a very high specific heat capacity. Therefore, water in the seas and oceans, heating up in summer, absorbs a large amount of heat from the air. Thanks to this, in those places that are located near large bodies of water, summer is not as hot as in places far from the water.

Calculation of the amount of heat required to heat a body or released by it during cooling.

From the above it is clear that the amount of heat required to heat a body depends on the type of substance of which the body consists (i.e., its specific heat capacity) and on the mass of the body. It is also clear that the amount of heat depends on how many degrees we are going to increase the body temperature.

So, to determine the amount of heat required to heat a body or released by it during cooling, you need to multiply the specific heat capacity of the body by its mass and by the difference between its final and initial temperatures:

Q = cm (t 2 - t 1 ) ,

Where Q- quantity of heat, c— specific heat capacity, m- body mass , t 1 — initial temperature, t 2 — final temperature.

When the body heats up t 2 > t 1 and therefore Q > 0 . When the body cools down t 2i< t 1 and therefore Q< 0 .

If the heat capacity of the entire body is known WITH, Q determined by the formula:

Q = C (t 2 - t 1 ) .

The content of the article

HEAT, the kinetic part of the internal energy of a substance, determined by the intense chaotic movement of the molecules and atoms of which this substance consists. Temperature is a measure of the intensity of molecular movement. The amount of heat possessed by a body at a given temperature depends on its mass; for example, at the same temperature, a large cup of water contains more heat than a small one, and a bucket of cold water may contain more heat than a cup of hot water (although the temperature of the water in the bucket is lower).

Warmth plays an important role in human life, including in the functioning of his body. Part of the chemical energy contained in food is converted into heat, due to which the body temperature is maintained around 37 ° C. The heat balance of the human body also depends on the ambient temperature, and people are forced to spend a lot of energy on heating residential and industrial premises in winter and on cooling them in summer. Most of this energy is supplied by heat engines, such as boilers and steam turbines in power plants that burn fossil fuels (coal, oil) and generate electricity.

Until the end of the 18th century. heat was considered a material substance, believing that the temperature of a body is determined by the amount of “caloric fluid” or “caloric” it contains. Later, B. Rumford, J. Joule and other physicists of that time, through ingenious experiments and reasoning, refuted the “caloric” theory, proving that heat is weightless and can be obtained in any quantity simply through mechanical movement. Heat itself is not a substance - it is just the energy of movement of its atoms or molecules. This is precisely the understanding of heat that modern physics adheres to.

In this article we will look at how heat and temperature are related and how these quantities are measured. The subject of our discussion will also be the following issues: transfer of heat from one part of the body to another; heat transfer in a vacuum (a space containing no substance); the role of heat in the modern world.

HEAT AND TEMPERATURE

The amount of thermal energy in a substance cannot be determined by observing the movement of each of its molecules individually. On the contrary, only by studying the macroscopic properties of a substance can one find the characteristics of the microscopic motion of many molecules averaged over a certain period of time. The temperature of a substance is the average indicator of the intensity of molecular motion, the energy of which is the thermal energy of the substance.

One of the most common, but also least accurate ways to assess temperature is by touch. When touching an object, we judge whether it is hot or cold, focusing on our sensations. Of course, these sensations depend on the temperature of our body, which brings us to the concept of thermal equilibrium - one of the most important when measuring temperature.

Thermal equilibrium.

Obviously, if two bodies A And B(Fig. 1) press tightly against each other, then, after touching them after a sufficiently long time, we will notice that their temperature is the same. In this case they say that the bodies A And B are in thermal equilibrium with each other. However, bodies, generally speaking, do not necessarily have to touch in order for thermal equilibrium to exist between them - it is enough that their temperatures are the same. This can be verified using the third body C, bringing it first into thermal equilibrium with the body A, and then comparing body temperatures C And B. Body C plays the role of a thermometer here. In a strict formulation, this principle is called the zero law of thermodynamics: if bodies A and B are in thermal equilibrium with a third body C, then these bodies are also in thermal equilibrium with each other. This law underlies all methods of measuring temperature.

Temperature measurement.

If we want to conduct accurate experiments and calculations, then such temperature ratings as hot, warm, cool, cold are not enough - we need a graduated temperature scale. There are several such scales, and the freezing and boiling temperatures of water are usually taken as reference points. The four most common scales are shown in Fig. 2. The centigrade scale, on which the freezing point of water corresponds to 0°, and the boiling point to 100°, is called the Celsius scale named after A. Celsius, the Swedish astronomer who described it in 1742. It is believed that the Swedish naturalist C. Linnaeus first used this scale . Now the Celsius scale is the most common in the world. The Fahrenheit temperature scale, in which the freezing and boiling points of water correspond to extremely inconvenient numbers of 32 and 212°, was proposed in 1724 by G. Fahrenheit. The Fahrenheit scale is widespread in English-speaking countries, but it is almost never used in scientific literature. To convert Celsius temperature (°C) to Fahrenheit temperature (°F) there is a formula °F = (9/5)°C + 32, and for the reverse conversion there is a formula °C = (5/9)(°F- 32).

Both scales - both Fahrenheit and Celsius - are very inconvenient when conducting experiments in conditions where the temperature drops below the freezing point of water and is expressed as a negative number. For such cases, absolute temperature scales were introduced, which are based on extrapolation to the so-called absolute zero - the point at which molecular motion should stop. One of them is called the Rankine scale, and the other is the absolute thermodynamic scale; their temperatures are measured in degrees Rankine (°R) and kelvins (K). Both scales begin at absolute zero, and the freezing point of water corresponds to 491.7° R and 273.16 K. The number of degrees and kelvins between the freezing and boiling points of water on the Celsius scale and the absolute thermodynamic scale are the same and equal to 100; for the Fahrenheit and Rankine scales it is also the same, but equal to 180. Degrees Celsius are converted to kelvins using the formula K = ° C + 273.16, and degrees Fahrenheit are converted to degrees Rankine using the formula ° R = ° F + 459.7.

The operation of instruments designed to measure temperature is based on various physical phenomena associated with changes in the thermal energy of a substance - changes in electrical resistance, volume, pressure, emissive characteristics, and thermoelectric properties. One of the simplest and most familiar instruments for measuring temperature is a mercury glass thermometer, shown in Fig. 3, A. A ball of mercury in the lower part of the thermometer is placed in a medium or pressed against an object whose temperature is to be measured, and depending on whether the ball receives or gives off heat, the mercury expands or contracts and its column rises or falls in the capillary. If the thermometer is pre-calibrated and equipped with a scale, then you can directly find out the body temperature.

Another device whose operation is based on thermal expansion is the bimetallic thermometer shown in Fig. 3, b. Its main element is a spiral plate made of two welded metals with different coefficients of thermal expansion. When heated, one of the metals expands more than the other, the spiral twists and turns the arrow relative to the scale. Such devices are often used to measure indoor and outdoor air temperatures, but are not suitable for determining local temperatures.

Local temperature is usually measured using a thermocouple, which is two wires of dissimilar metals soldered at one end (Fig. 4, A). When such a junction is heated, an emf is generated at the free ends of the wires, usually amounting to several millivolts. Thermocouples are made from different metal pairs: iron and constantan, copper and constantan, chromel and alumel. Their thermo-emf varies almost linearly with temperature over a wide temperature range.

Another thermoelectric effect is also known - the dependence of the resistance of a conductive material on temperature. It underlies the operation of electrical resistance thermometers, one of which is shown in Fig. 4, b. The resistance of a small temperature-sensitive element (thermal transducer) - usually a coil of thin wire - is compared with the resistance of a calibrated variable resistor using a Wheatstone bridge. The output device can be calibrated directly in degrees.

Optical pyrometers are used to measure the temperature of hot bodies emitting visible light. In one embodiment of this device, the light emitted by the body is compared with the emission of an incandescent lamp filament placed in the focal plane of binoculars through which the emitting body is viewed. The electric current heating the lamp filament is changed until a visual comparison of the glow of the filament and the body reveals that thermal equilibrium has been established between them. The instrument scale can be calibrated directly in temperature units.

Measuring the amount of heat.

The thermal energy (amount of heat) of a body can be measured directly using a so-called calorimeter; a simple version of such a device is shown in Fig. 5. This is a carefully insulated closed vessel, equipped with devices for measuring the temperature inside it and sometimes filled with a working fluid with known properties, such as water. To measure the amount of heat in a small heated body, it is placed in a calorimeter and the system is waited until it reaches thermal equilibrium. The amount of heat transferred to the calorimeter (more precisely, to the water filling it) is determined by the increase in water temperature.

The amount of heat released during a chemical reaction, such as combustion, can be measured by placing a small “bomb” in a calorimeter. The “bomb” contains a sample, to which electrical wires are connected for ignition, and an appropriate amount of oxygen. After the sample burns completely and thermal equilibrium is established, it is determined how much the temperature of the water in the calorimeter has increased, and hence the amount of heat released.

Units of heat measurement.

Heat is a form of energy and therefore must be measured in energy units. The SI unit of energy is the joule (J). It is also possible to use non-systemic units of the amount of heat - calories: the international calorie is 4.1868 J, the thermochemical calorie - 4.1840 J. In foreign laboratories, research results are often expressed using the so-called. A 15-degree calorie equals 4.1855 J. The off-system British thermal unit (BTU) is being phased out: BTU avg = 1.055 J.

Sources of heat.

The main sources of heat are chemical and nuclear reactions, as well as various energy conversion processes. Examples of chemical reactions that release heat are combustion and the breakdown of food components. Almost all the heat received by the Earth is provided by nuclear reactions occurring in the depths of the Sun. Humanity has learned to obtain heat using controlled nuclear fission processes, and is now trying to use thermonuclear fusion reactions for the same purpose. Other types of energy, such as mechanical work and electrical energy, can also be converted into heat. It is important to remember that thermal energy (like any other) can only be converted into another form, but cannot be obtained “out of nothing” or destroyed. This is one of the basic principles of the science called thermodynamics.

THERMODYNAMICS

Thermodynamics is the science of the relationship between heat, work and matter. Modern ideas about these relationships were formed on the basis of the works of such great scientists of the past as Carnot, Clausius, Gibbs, Joule, Kelvin, etc. Thermodynamics explains the meaning of heat capacity and thermal conductivity of matter, thermal expansion of bodies, and the heat of phase transitions. This science is based on several experimentally established laws - principles.

The beginnings of thermodynamics.

The zero law of thermodynamics formulated above introduces the concepts of thermal equilibrium, temperature and thermometry. The first law of thermodynamics is a statement that is of key importance for all science as a whole: energy can neither be destroyed nor obtained “out of nothing,” so the total energy of the Universe is a constant quantity. In its simplest form, the first law of thermodynamics can be stated as follows: the energy a system receives minus the energy it gives out equals the energy remaining in the system. At first glance, this statement seems obvious, but not in such a situation, for example, as the combustion of gasoline in the cylinders of a car engine: here the energy received is chemical, the energy given is mechanical (work), and the energy remaining in the system is thermal.

So, it is clear that energy can transform from one form to another and that such transformations constantly occur in nature and technology. More than a hundred years ago, J. Joule proved this for the case of converting mechanical energy into thermal energy using the device shown in Fig. 6, A. In this device, descending and rising weights rotated a shaft with blades in a water-filled calorimeter, causing the water to heat up. Precise measurements allowed Joule to determine that one calorie of heat is equivalent to 4.186 J of mechanical work. The device shown in Fig. 6, b, was used to determine the thermal equivalent of electrical energy.

The first law of thermodynamics explains many everyday phenomena. For example, it becomes clear why you cannot cool the kitchen with an open refrigerator. Let's assume that we have insulated the kitchen from the environment. Energy is continuously supplied to the system through the refrigerator's power wire, but the system does not release any energy. Thus, its total energy increases, and the kitchen becomes increasingly warmer: just touch the heat exchanger (condenser) tubes on the back wall of the refrigerator, and you will understand the uselessness of it as a “cooling” device. But if these tubes were taken outside the system (for example, outside the window), then the kitchen would give out more energy than it received, i.e. would cool, and the refrigerator would work like a window air conditioner.

The first law of thermodynamics is a law of nature that excludes the creation or destruction of energy. However, it says nothing about how energy transfer processes occur in nature. So, we know that a hot body will heat a cold one if these bodies are brought into contact. But can a cold body by itself transfer its heat reserve to a hot one? The latter possibility is categorically rejected by the second law of thermodynamics.

The first principle also excludes the possibility of creating an engine with a coefficient of performance (efficiency) of more than 100% (such a “perpetual” engine could, for any length of time, supply more energy than it consumes). It is impossible to build an engine even with an efficiency of 100%, since some part of the energy supplied to it must necessarily be lost by it in the form of less useful thermal energy. Thus, the wheel will not spin for any length of time without energy supply, since due to friction in the bearings, the energy of mechanical movement will gradually turn into heat until the wheel stops.

The tendency to convert "useful" work into less useful energy - heat - can be compared with another process that occurs when two vessels containing different gases are connected. Having waited long enough, we find a homogeneous mixture of gases in both vessels - nature acts in such a way that the order of the system decreases. The thermodynamic measure of this disorder is called entropy, and the second law of thermodynamics can be formulated differently: processes in nature always proceed in such a way that the entropy of the system and its environment increases. Thus, the energy of the Universe remains constant, but its entropy continuously increases.

Heat and properties of substances.

Different substances have different abilities to store thermal energy; this depends on their molecular structure and density. The amount of heat required to raise the temperature of a unit mass of a substance by one degree is called its specific heat capacity. Heat capacity depends on the conditions in which the substance is located. For example, to heat one gram of air in a balloon by 1 K, more heat is required than for the same heating in a sealed vessel with rigid walls, since part of the energy imparted to the balloon is spent on expanding the air, and not on heating it. Therefore, in particular, the heat capacity of gases is measured separately at constant pressure and at constant volume.

As the temperature rises, the intensity of the chaotic movement of molecules increases - most substances expand when heated. The degree of expansion of a substance when the temperature increases by 1 K is called the coefficient of thermal expansion.

In order for a substance to move from one phase state to another, for example from solid to liquid (and sometimes directly to gaseous), it must receive a certain amount of heat. If you heat a solid, its temperature will increase until it begins to melt; until melting is complete, the body temperature will remain constant, despite the addition of heat. The amount of heat required to melt a unit mass of a substance is called the heat of fusion. If you apply heat further, the molten substance will heat to a boil. The amount of heat required to evaporate a unit mass of liquid at a given temperature is called the heat of vaporization.

Molecular kinetic theory.

The molecular kinetic theory explains the macroscopic properties of a substance by considering at the microscopic level the behavior of the atoms and molecules that make up this substance. In this case, a statistical approach is used and some assumptions are made regarding the particles themselves and the nature of their movement. Thus, molecules are considered to be solid balls, which in gaseous media are in continuous chaotic motion and cover considerable distances from one collision to another. Collisions are considered elastic and occur between particles whose size is small but their number is very large. None of the real gases corresponds exactly to this model, but most gases are quite close to it, which determines the practical value of the molecular kinetic theory.

Based on these ideas and using a statistical approach, Maxwell derived the distribution of velocities of gas molecules in a limited volume, which was later named after him. This distribution is presented graphically in Fig. 7 for a certain given mass of hydrogen at temperatures of 100 and 1000 ° C. The number of molecules moving at the speed indicated on the abscissa is plotted along the ordinate axis. The total number of particles is equal to the area under each curve and is the same in both cases. The graph shows that most particles have velocities close to some average value, and only a small number have very high or low velocities. Average velocities at the indicated temperatures lie in the range of 2000–3000 m/s, i.e. very large.

A large number of such fast moving gas molecules acts with quite measurable force on the surrounding bodies. The microscopic forces with which numerous gas molecules strike the walls of the container add up to a macroscopic quantity called pressure. When energy is supplied to a gas (temperature increases), the average kinetic energy of its molecules increases, gas particles hit the walls more often and harder, the pressure increases, and if the walls are not completely rigid, then they stretch and the volume of the gas increases. Thus, the microscopic statistical approach underlying the molecular kinetic theory allows us to explain the phenomenon of thermal expansion that we discussed.

Another result of the molecular kinetic theory is a law that describes the properties of a gas that satisfies the requirements listed above. This so-called ideal gas equation of state relates the pressure, volume and temperature of one mole of gas and has the form

PV = RT,

Where P- pressure, V- volume, T– temperature, and R– universal gas constant equal to (8.31441 ± 0.00026) J/(mol K). THERMODYNAMICS.

HEAT TRANSFER

Heat transfer is the process of transferring heat within a body or from one body to another due to temperature differences. The intensity of heat transfer depends on the properties of the substance, the temperature difference and obeys the experimentally established laws of nature. To create efficiently operating heating or cooling systems, various engines, power plants, and thermal insulation systems, you need to know the principles of heat transfer. In some cases, heat exchange is undesirable (thermal insulation of smelting furnaces, spaceships, etc.), while in others it should be as large as possible (steam boilers, heat exchangers, kitchen utensils).

There are three main types of heat transfer: conduction, convection and radiant heat transfer.

Thermal conductivity.

If there is a temperature difference inside the body, then thermal energy moves from the hotter part of the body to the colder part. This type of heat transfer, caused by thermal movements and collisions of molecules, is called thermal conductivity; at sufficiently high temperatures in solids it can be observed visually. Thus, when a steel rod is heated from one end in the flame of a gas burner, thermal energy is transferred along the rod, and a glow spreads over a certain distance from the heated end (ever less intense with distance from the place of heating).

The intensity of heat transfer due to thermal conductivity depends on the temperature gradient, i.e. relationship D T/D x temperature difference at the ends of the rod to the distance between them. It also depends on the cross-sectional area of the rod (in m2) and the thermal conductivity coefficient of the material [in the corresponding units of W/(mH K)]. The relationship between these quantities was derived by the French mathematician J. Fourier and has the following form:

Where q– heat flow, k is the thermal conductivity coefficient, and A– cross-sectional area. This relationship is called Fourier's law of thermal conductivity; the minus sign in it indicates that heat is transferred in the direction opposite to the temperature gradient.

From Fourier's law it follows that heat flow can be reduced by reducing one of the quantities - thermal conductivity coefficient, area or temperature gradient. For a building in winter conditions, the latter values are practically constant, and therefore, in order to maintain the desired temperature in the room, it remains to reduce the thermal conductivity of the walls, i.e. improve their thermal insulation.

The table shows the thermal conductivity coefficients of some substances and materials. The table shows that some metals conduct heat much better than others, but all of them are significantly better conductors of heat than air and porous materials.

THERMAL CONDUCTIVITY OF SOME SUBSTANCES AND MATERIALS
Substances and materials	Thermal conductivity, W/(m× K)
Metals
Aluminum
Bronze
Bismuth
Tungsten
Iron
Gold
Cadmium
Magnesium
Copper
Arsenic
Nickel
Platinum
Mercury
Lead
Zinc
Other materials
Asbestos
Concrete
Air
Eider down (loose)
Tree nut)
Magnesia (MgO)
Sawdust
Rubber (sponge)
Mica
Glass
Carbon (graphite)

The thermal conductivity of metals is due to vibrations of the crystal lattice and the movement of a large number of free electrons (sometimes called electron gas). The movement of electrons is also responsible for the electrical conductivity of metals, so it is not surprising that good conductors of heat (for example, silver or copper) are also good conductors of electricity.

The thermal and electrical resistance of many substances decreases sharply as the temperature drops below the temperature of liquid helium (1.8 K). This phenomenon, called superconductivity, is used to improve the efficiency of many devices - from microelectronics devices to power lines and large electromagnets.

Convection.

As we have already said, when heat is supplied to a liquid or gas, the intensity of molecular movement increases, and as a result, the pressure increases. If a liquid or gas is not limited in volume, then it expands; the local density of the liquid (gas) becomes smaller, and thanks to buoyancy (Archimedean) forces, the heated part of the medium moves upward (which is why the warm air in the room rises from the radiators to the ceiling). This phenomenon is called convection. In order not to waste the heat of the heating system, you need to use modern heaters that provide forced air circulation.

Convective heat flow from the heater to the heated medium depends on the initial speed of movement of molecules, density, viscosity, thermal conductivity and heat capacity and the medium; The size and shape of the heater are also very important. The relationship between the corresponding quantities obeys Newton's law

q = hA (T W - T Ґ ),

Where q– heat flow (measured in watts), A– surface area of the heat source (in m2), T W And TҐ – temperatures of the source and its environment (in Kelvin). Convective heat transfer coefficient h depends on the properties of the medium, the initial speed of its molecules, as well as on the shape of the heat source, and is measured in units of W/(m 2 H K).

Magnitude h is not the same for the cases when the air around the heater is stationary (free convection) and when the same heater is in an air flow (forced convection). In simple cases of fluid flow through a pipe or flow around a flat surface, the coefficient h can be calculated theoretically. However, it has not yet been possible to find an analytical solution to the problem of convection for a turbulent flow of a medium. Turbulence is a complex movement of a liquid (gas), chaotic on a scale significantly larger than the molecular one.

If a heated (or, conversely, cold) body is placed in a stationary medium or in a flow, then convective currents and a boundary layer are formed around it. Temperature, pressure and the speed of movement of molecules in this layer play an important role in determining the coefficient of convective heat transfer.

Convection must be taken into account in the design of heat exchangers, air conditioning systems, high-speed aircraft and many other applications. In all such systems, thermal conductivity occurs simultaneously with convection, both between solid bodies and in their environment. At elevated temperatures, radiant heat transfer can also play a significant role.

Radiant heat transfer.

The third type of heat transfer - radiant heat transfer - differs from thermal conductivity and convection in that heat in this case can be transferred through a vacuum. Its similarity with other methods of heat transfer is that it is also caused by temperature differences. Thermal radiation is a type of electromagnetic radiation. Its other types - radio wave, ultraviolet and gamma radiation - arise in the absence of a temperature difference.

In Fig. Figure 8 shows the dependence of the energy of thermal (infrared) radiation on the wavelength. Thermal radiation can be accompanied by the emission of visible light, but its energy is small compared to the energy of radiation from the invisible part of the spectrum.

The intensity of heat transfer by conduction and convection is proportional to temperature, and radiant heat flow is proportional to the fourth power of temperature and obeys the Stefan–Boltzmann law

where, as before, q– heat flow (in joules per second, i.e. in W), A is the surface area of the radiating body (in m2), and T 1 and T 2 – temperatures (in Kelvin) of the radiating body and the environment absorbing this radiation. Coefficient s is called the Stefan–Boltzmann constant and is equal to (5.66961 ± 0.00096) H 10 –8 W/(m 2 H K 4).

The presented law of thermal radiation is valid only for an ideal emitter - the so-called absolutely black body. No real body is like this, although a flat black surface in its properties approaches an absolutely black body. Light surfaces emit relatively weakly. To take into account the deviation from ideality of numerous “gray” bodies, a coefficient less than unity, called emissivity, is introduced into the right side of the expression describing the Stefan-Boltzmann law. For a flat black surface this coefficient can reach 0.98, and for a polished metal mirror it does not exceed 0.05. Accordingly, the radiation absorption capacity is high for a black body and low for a mirror body.

Residential and office spaces are often heated with small electric heat emitters; the reddish glow of their spirals is visible thermal radiation, close to the edge of the infrared part of the spectrum. The room is heated by heat, which is carried mainly by the invisible, infrared part of the radiation. Night vision devices use a thermal radiation source and an infrared-sensitive receiver to allow vision in the dark.

The Sun is a powerful emitter of thermal energy; it heats the Earth even at a distance of 150 million km. The intensity of solar radiation recorded year after year by stations located in many parts of the globe is approximately 1.37 W/m2. Solar energy is the source of life on Earth. The search for ways to use it most effectively is underway. Solar panels have been created to heat houses and generate electricity for domestic needs.

ROLE OF HEAT AND ITS USE

The transfer of heat (due to thermal conductivity) from the molten core of the Earth to its surface leads to volcanic eruptions and the appearance of geysers. In some regions, geothermal energy is used for space heating and electricity generation.

Heat is an indispensable participant in almost all production processes. Let us mention the most important of them, such as smelting and processing of metals, engine operation, food production, chemical synthesis, oil refining, and the manufacture of a wide variety of items - from bricks and dishes to cars and electronic devices.

Many industrial production and transport, as well as thermal power plants, could not operate without heat engines - devices that convert heat into useful work. Examples of such machines include compressors, turbines, steam, gasoline and jet engines.

One of the most famous heat engines is the steam turbine, which implements part of the Rankine cycle used in modern power plants. A simplified diagram of this cycle is shown in Fig. 9. The working fluid - water - is converted into superheated steam in a steam boiler, heated by burning fossil fuels (coal, oil or natural gas). High-pressure steam rotates the shaft of a steam turbine, which drives a generator that produces electricity. The exhaust steam condenses when cooled by running water, which absorbs some of the heat not used in the Rankine cycle. Next, the water is supplied to the cooling tower, from where part of the heat is released into the atmosphere. The condensate is returned to the steam boiler using a pump, and the entire cycle is repeated.

All processes in the Rankine cycle illustrate the principles of thermodynamics described above. In particular, according to the second law, part of the energy consumed by a power plant must be dissipated in the environment in the form of heat. It turns out that approximately 68% of the energy originally contained in fossil fuels is lost in this way. A noticeable increase in the efficiency of a power plant could be achieved only by increasing the temperature of the steam boiler (which is limited by the heat resistance of the materials) or lowering the temperature of the medium where the heat goes, i.e. atmosphere.

Another thermodynamic cycle that is of great importance in our daily life is the Rankine vapor-compressor refrigeration cycle, the diagram of which is shown in Fig. 10. In refrigerators and household air conditioners, energy to provide it is supplied from the outside. The compressor increases the temperature and pressure of the refrigerator’s working substance – freon, ammonia or carbon dioxide. The superheated gas is supplied to the condenser, where it cools and condenses, releasing heat to the environment. The liquid leaving the condenser pipes passes through the throttling valve into the evaporator, and part of it evaporates, which is accompanied by a sharp drop in temperature. The evaporator takes heat from the refrigerator chamber, which heats the working fluid in the pipes; this liquid is supplied by the compressor to the condenser, and the cycle repeats again.

The refrigeration cycle shown in Fig. 10, can also be used in a heat pump. Such heat pumps in summer give off heat to hot atmospheric air and condition the room, and in winter, on the contrary, they take heat from cold air and heat the room.

Nuclear reactions are an important source of heat for purposes such as power generation and transportation. In 1905 A. Einstein showed that mass and energy are related by the relation E=mc 2, i.e. can transform into each other. Speed of light c very high: 300 thousand km/s. This means that even a small amount of a substance can provide a huge amount of energy. Thus, from 1 kg of fissile material (for example, uranium), it is theoretically possible to obtain the energy that a 1 MW power plant provides in 1000 days of continuous operation.

Definition

The amount of heat or simply warmth($Q$) is the internal energy that, without performing work, is transferred from bodies with a higher temperature to bodies with a lower temperature in the processes of thermal conductivity or radiation.

Joule is a unit of measurement of the amount of heat in the SI system

The unit of heat can be obtained from the first law of thermodynamics:

\[\Delta Q=A+\Delta U\ \left(1\right),\]

where $A$ is the work of the thermodynamic system; $\Delta U$ - change in the internal energy of the system; $\Delta Q$ is the amount of heat supplied to the system.

From law (1), and even more so from its version for an isothermal process:

\[\Delta Q=A\ \left(2\right).\]

Obviously, in the International System of Units (SI), the joule (J) is a unit of energy and work.

It is easy to express the joule in basic units if we use the definition of energy ($E$) of the form:

where $c$ is the speed of light; $m$ is body weight. Based on expression (2), we have:

\[\left=\left=kg\cdot (\left(\frac(m)(s)\right))^2=\frac(kg\cdot m^2)(s^2).\]

All standard SI prefixes are used with the joule, denoting decimal submultiples and multiples. For example, $1kJ=(10)^3J$; 1MJ =$(10)^6J$; 1 GJ=$(10)^9J$.

Erg is a unit of measurement of the amount of heat in the CGS system

In the CGS system (centimeter, gram, second), heat is measured in ergs (erg). In this case, one erg is equal to:

Taking into account that:

we get the relationship between joule and erg:

Calorie - a unit of measurement of the amount of heat

The calorie is used as an off-system unit for measuring the amount of heat. One calorie is equal to the amount of heat that must be transferred to water weighing one kilogram to heat it by one degree Celsius. The relationship between joule and calorie is as follows:

To be more precise, they distinguish:

International calorie, it is equal to:
thermochemical calorie:
15 degree calorie used for thermal measurements:

Calories are often used with decimal prefixes, such as: kcal (kilocalorie) $1kcal=(10)^3cal$; Mcal (megacalorie) 1 Mcal =$(10)^6cal$; Gcal (gigacalorie) 1 Gcal=$(10)^9cal$.

Sometimes a kilocalorie is called a large calorie or a kilocalorie.

Examples of problems with solutions

Example 1

Exercise. How much heat is absorbed by hydrogen weighing $m=0.2$kg when it is heated from $t_1=0(\rm()^\circ\!C)$ to $t_2=100(\rm()^\circ\! C)$ at constant pressure? Write your answer in kilojoules.

Solution. Let's write down the first law of thermodynamics:

\[\Delta Q=A+\Delta U\ \left(1.1\right).\]

\[\Delta U=\frac(i)(2)\frac(m)(\mu )R\Delta T\ \left(1.2\right),\]

where $i=5$ is the number of degrees of freedom of the hydrogen molecule; $\mu =2\cdot (10)^(-3)\frac(kg)(mol)$; $R=8.31\ \frac(J)(mol\cdot K)$; $\Delta T=t_2-t_1$. By condition, we are dealing with an isobaric process. Work in an isobaric process is equal to:

Taking into account expressions (1.2) and (1.3), we transform the first law of thermodynamics for an isobaric process to the form:

\[\Delta Q=\frac(m)(\mu )R\Delta T\ +\frac(i)(2)\frac(m)(\mu )R\Delta T=\frac(m)(\ mu )R\Delta T\left(1+\frac(i)(2)\right)\ \left(1.4\right).\]

Let's check in what units heat is measured if it is calculated using formula (1.4):

\[\left[\Delta Q\right]=\left[\frac(m)(\mu )R\Delta T\left(1+\frac(i)(2)\right)\right]=\left [\frac(m)(\mu )R\Delta T\right]=\frac(\left)(\left[\mu \right])\left\left[\Delta T\right]=\frac(kg )(kg/mol)\cdot \frac(J)(mol\cdot K)\cdot K=J.\]

Let's carry out the calculations:

\[\Delta Q=\frac(0.2)(2 (10)^(-3))\cdot 8.31\cdot 100\left(1+\frac(5)(2)\right)\approx 291\cdot (10)^3\left(J\right)=291\ \left(kJ\right).\]

Answer.$\Delta Q=291\ $ kJ

Example 2

Exercise. Helium, having a mass of $m=1\ g$, was heated by 100 K in the process shown in Fig. 1. How much heat is transferred to the gas? Write your answer in GHS units.

Solution. Figure 1 shows an isochoric process. For such a process we write the first law of thermodynamics as:

\[\Delta Q=\Delta U\ \left(2.1\right).\]

We find the change in internal energy as:

\[\Delta U=\frac(i)(2)\frac(m)(\mu )R\Delta T\ \left(2.2\right),\]

where $i=3$ is the number of degrees of freedom of a helium molecule; $\mu =4\frac(g)(mol)$; $R=8.31\cdot (10)^7\ \frac(erg)(mol\cdot K)$; $\Delta T=100\ K.$ All values are written in the SGS. Let's carry out the calculations:

\[\Delta Q=\frac(3)(2)\cdot \frac(1)(4)\cdot 8.31\cdot (10)^7\cdot 100\approx 3\cdot (10)^9( erg)\ \]

Answer.$\Delta Q=3\cdot (10)^9$ erg

Thermal energy is a system for measuring heat that was invented and used two centuries ago. The basic rule for working with this value was that thermal energy is conserved and cannot simply disappear, but can be transformed into another type of energy.

There are several generally accepted units of thermal energy. They are mainly used in industrial sectors such as. The most common ones are described below:

Any unit of measurement included in the SI system has a purpose in determining the total amount of one or another type of energy, such as heat or electricity. The measurement time and quantity do not affect these values, which is why they can be used for both consumed and already consumed energy. In addition, any transmission and reception, as well as losses, are also calculated in such quantities.

Where are the units of measurement of thermal energy used?

Energy units converted to heat

For illustrative purposes, below are comparisons of various popular SI indices with thermal energy:

1 GJ is equal to 0.24 Gcal, which in electrical equivalent is equal to 3400 million kW per hour. In thermal energy equivalent, 1 GJ = 0.44 tons of steam;
At the same time, 1 Gcal = 4.1868 GJ = 16,000 million kW per hour = 1.9 tons of steam;
1 ton of steam equals 2.3 GJ = 0.6 Gcal = 8200 kW per hour.

In this example, the given value of steam is taken as the evaporation of water upon reaching 100°C.

To calculate the amount of heat, the following principle is used: to obtain data on the amount of heat, it is used in heating the liquid, after which the mass of water is multiplied by the germination temperature. If in SI the mass of a liquid is measured in kilograms, and temperature differences in degrees Celsius, then the result of such calculations will be the amount of heat in kilocalories.

If there is a need to transfer thermal energy from one physical body to another, and you want to find out the possible losses, then you should multiply the mass of the substance’s heat received by the temperature of the increase, and then find out the product of the resulting value by the “specific heat” of the substance.