Along with mechanical energy, any body (or system) has internal energy. Internal energy is rest energy. It consists of the thermal chaotic motion of the molecules that make up the body, the potential energy of their relative position, the kinetic and potential energy of electrons in atoms, nucleons in nuclei, and so on.
In thermodynamics, it is important to know not the absolute value of internal energy, but its change.
In thermodynamic processes, only the kinetic energy of moving molecules changes (thermal energy is not enough to change the structure of an atom, and even more so of a nucleus). Therefore, in fact under internal energy in thermodynamics means energy thermal chaotic molecular movements.
Internal energy U one mole of an ideal gas is equal to:
In this way, internal energy depends only on temperature. The internal energy U is a function of the state of the system, regardless of background.
It is clear that, in the general case, a thermodynamic system can have both internal and mechanical energy, and different systems can exchange these types of energy.
Exchange mechanical energy characterized by perfect work A, and the exchange of internal energy - the amount of heat transferred Q.
For example, in winter you threw a hot stone into the snow. Due to the reserve of potential energy, mechanical work was done to crush the snow, and due to the reserve of internal energy, the snow was melted. If the stone was cold, i.e. the temperature of the stone is equal to the temperature of the environment, then only work will be done, but there will be no exchange of internal energy.
So, work and heat are not special forms of energy. You can not talk about the stock of heat or work. it measure transferred another system of mechanical or internal energy. We can talk about the reserve of these energies. In addition, mechanical energy can be converted into thermal energy and vice versa. For example, if you hit an anvil with a hammer, then after a while the hammer and anvil will heat up (this is an example dissipation energy).
There are many more examples of the transformation of one form of energy into another.
Experience shows that in all cases, the transformation of mechanical energy into thermal energy and vice versa is always carried out in strictly equivalent quantities. This is the essence of the first law of thermodynamics, which follows from the law of conservation of energy.
The amount of heat imparted to the body is used to increase internal energy and to perform work on the body:
| , | (4.1.1) |
- That's what it is first law of thermodynamics , or law of conservation of energy in thermodynamics.
Sign rule: if heat is transferred from the environment this system, and if the system performs work on the surrounding bodies, while . Given the sign rule, the first law of thermodynamics can be written as:
In this expression U is the system state function; d U is its total differential, and δ Q and δ BUT they are not. In each state, the system has a certain and only such value of internal energy, so we can write:
 ,
|
It is important to note that the heat Q and work BUT depend on how the transition from state 1 to state 2 is made (isochoric, adiabatic, etc.), and the internal energy U does not depend. At the same time, it cannot be said that the system has a value of heat and work determined for a given state.
From formula (4.1.2) it follows that the amount of heat is expressed in the same units as work and energy, i.e. in joules (J).
Of particular importance in thermodynamics are circular or cyclic processes in which the system, after passing through a series of states, returns to its original state. Figure 4.1 shows a cyclic process 1– a–2–b–1, while work A was done.
Rice. 4.1
Because U is the state function, then
| (4.1.3) |
This is true for any state function.
If then according to the first law of thermodynamics, i.e. it is impossible to build a periodically operating engine that would do more work than the amount of energy imparted to it from outside. In other words, a perpetual motion machine of the first kind is impossible. This is one of the formulations of the first law of thermodynamics.
It should be noted that the first law of thermodynamics does not indicate in which direction the processes of state change go, which is one of its shortcomings.
« Physics - Grade 10 "
In what processes does aggregate transformation of matter occur?
How can the state of matter be changed?
You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
Thus, when forging a metal, work is done and it is heated, while at the same time the metal can be heated over a burning flame.
Also, if the piston is fixed (Fig. 13.5), then the volume of gas does not change when heated and no work is done. But the temperature of the gas, and hence its internal energy, increases.
Internal energy can increase and decrease, so the amount of heat can be positive or negative.
The process of transferring energy from one body to another without doing work is called heat exchange.
The quantitative measure of the change in internal energy during heat transfer is called amount of heat.
Molecular picture of heat transfer.
During heat exchange at the boundary between bodies, slowly moving molecules of a cold body interact with rapidly moving molecules of a hot body. As a result, the kinetic energies of the molecules are equalized and the velocities of the molecules of a cold body increase, while those of a hot body decrease.
During heat exchange, there is no conversion of energy from one form to another; part of the internal energy of a hotter body is transferred to a less heated body.
The amount of heat and heat capacity.
You already know that in order to heat a body with mass m from temperature t 1 to temperature t 2, it is necessary to transfer to it the amount of heat:
Q \u003d cm (t 2 - t 1) \u003d cm Δt. (13.5)
When the body cools, its final temperature t 2 turns out to be less than the initial temperature t 1 and the amount of heat given off by the body is negative.
The coefficient c in formula (13.5) is called specific heat capacity substances.
Specific heat- this is a value numerically equal to the amount of heat that a substance with a mass of 1 kg receives or gives off when its temperature changes by 1 K.
The specific heat capacity of gases depends on the process by which heat is transferred. If you heat a gas at constant pressure, it will expand and do work. To heat a gas by 1 °C at constant pressure, it needs to transfer more heat than to heat it at a constant volume, when the gas will only heat up.
Liquids and solids expand slightly when heated. Their specific heat capacities at constant volume and constant pressure differ little.
Specific heat of vaporization.
To convert a liquid into vapor during the boiling process, it is necessary to transfer a certain amount of heat to it. The temperature of a liquid does not change when it boils. The transformation of liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of molecules, but is accompanied by an increase in the potential energy of their interaction. After all, the average distance between gas molecules is much greater than between liquid molecules.
The value numerically equal to the amount of heat required to convert a 1 kg liquid into steam at a constant temperature is called specific heat of vaporization.
The process of liquid evaporation occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of vaporization is equal to the specific heat of vaporization.
This value is denoted by the letter r and is expressed in joules per kilogram (J / kg).
The specific heat of vaporization of water is very high: r H20 = 2.256 10 6 J/kg at a temperature of 100 °C. In other liquids, such as alcohol, ether, mercury, kerosene, the specific heat of vaporization is 3-10 times less than that of water.
To convert a liquid of mass m into steam, an amount of heat is required equal to:
Q p \u003d rm. (13.6)
When steam condenses, the same amount of heat is released:
Q k \u003d -rm. (13.7)
Specific heat of fusion.
When a crystalline body melts, all the heat supplied to it goes to increase the potential energy of interaction of molecules. The kinetic energy of the molecules does not change, since melting occurs at a constant temperature.
The value numerically equal to the amount of heat required to transform a crystalline substance weighing 1 kg at a melting point into a liquid is called specific heat of fusion and are denoted by the letter λ.
During the crystallization of a substance with a mass of 1 kg, exactly the same amount of heat is released as is absorbed during melting.
The specific heat of melting of ice is rather high: 3.34 10 5 J/kg.
“If ice did not have a high heat of fusion, then in spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to ice from the air. The consequences of this would be dire; for even under the present situation great floods and great torrents of water arise from the melting of great masses of ice or snow.” R. Black, 18th century
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl \u003d λm. (13.8)
The amount of heat released during the crystallization of the body is equal to:
Q cr = -λm (13.9)
Heat balance equation.
Consider heat exchange within a system consisting of several bodies initially having different temperatures, for example, heat exchange between water in a vessel and a hot iron ball lowered into water. According to the law of conservation of energy, the amount of heat given off by one body is numerically equal to the amount of heat received by another.
The given amount of heat is considered negative, the received amount of heat is considered positive. Therefore, the total amount of heat Q1 + Q2 = 0.
If heat exchange occurs between several bodies in an isolated system, then
Q 1 + Q 2 + Q 3 + ... = 0. (13.10)
Equation (13.10) is called heat balance equation.
Here Q 1 Q 2 , Q 3 - the amount of heat received or given away by the bodies. These quantities of heat are expressed by formula (13.5) or formulas (13.6) - (13.9), if various phase transformations of the substance occur in the process of heat transfer (melting, crystallization, vaporization, condensation).
The internal energy of a thermodynamic system can be changed in two ways:
- doing work on the system
- through thermal interaction.
The transfer of heat to a body is not connected with the performance of macroscopic work on the body. In this case, the change in internal energy is caused by the fact that individual molecules of the body with a higher temperature do work on some molecules of the body, which has a lower temperature. In this case, thermal interaction is realized due to thermal conduction. The transfer of energy is also possible with the help of radiation. The system of microscopic processes (pertaining not to the whole body, but to individual molecules) is called heat transfer. The amount of energy that is transferred from one body to another as a result of heat transfer is determined by the amount of heat that is transferred from one body to another.
Definition
warmth called the energy that is received (or given away) by the body in the process of heat exchange with the surrounding bodies (environment). Heat is denoted, usually by the letter Q.
This is one of the basic quantities in thermodynamics. Heat is included in the mathematical expressions of the first and second laws of thermodynamics. Heat is said to be energy in the form of molecular motion.
Heat can be communicated to the system (body), or it can be taken from it. It is believed that if heat is imparted to the system, then it is positive.
The formula for calculating heat with a change in temperature
The elementary amount of heat is denoted as . Note that the element of heat that the system receives (gives off) with a small change in its state is not a total differential. The reason for this is that heat is a function of the process of changing the state of the system.
The elementary amount of heat that is reported to the system, and the temperature changes from T to T + dT, is:
where C is the heat capacity of the body. If the body under consideration is homogeneous, then formula (1) for the amount of heat can be represented as:
where is the specific heat of the body, m is the mass of the body, is the molar heat capacity, is the molar mass of the substance, is the number of moles of the substance.
If the body is homogeneous, and the heat capacity is considered independent of temperature, then the amount of heat () that the body receives when its temperature increases by a value can be calculated as:
where t 2 , t 1 body temperature before and after heating. Please note that when finding the difference () in the calculations, temperatures can be substituted both in degrees Celsius and in kelvins.
The formula for the amount of heat during phase transitions
The transition from one phase of a substance to another is accompanied by the absorption or release of a certain amount of heat, which is called the heat of the phase transition.
So, to transfer an element of matter from a solid state to a liquid, it should be informed of the amount of heat () equal to:
where is the specific heat of fusion, dm is the body mass element. In this case, it should be taken into account that the body must have a temperature equal to the melting point of the substance in question. During crystallization, heat is released equal to (4).
The amount of heat (heat of vaporization) required to convert liquid to vapor can be found as:
where r is the specific heat of vaporization. When steam condenses, heat is released. The heat of evaporation is equal to the heat of condensation of equal masses of matter.
Units for measuring the amount of heat
The basic unit for measuring the amount of heat in the SI system is: [Q]=J
An off-system unit of heat that is often found in technical calculations. [Q]=cal (calorie). 1 cal = 4.1868 J.
Examples of problem solving
Example
Exercise. What volumes of water should be mixed to obtain 200 liters of water at a temperature of t=40C, if the temperature of one mass of water is t 1 =10C, the second mass of water is t 2 =60C?
Solution. We write the heat balance equation in the form:
where Q=cmt - the amount of heat prepared after mixing water; Q 1 \u003d cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 \u003d cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.
Equation (1.1) implies:
When combining cold (V 1) and hot (V 2) parts of water into a single volume (V), we can accept that:
So, we get a system of equations:
Solving it, we get:
The focus of our article is the amount of heat. We will consider the concept of internal energy, which is transformed when this value changes. We will also show some examples of the application of calculations in human activity.
Heat
With any word of the native language, each person has his own associations. They are determined by personal experience and irrational feelings. What is usually represented by the word "warmth"? A soft blanket, a working central heating battery in winter, the first sunlight in spring, a cat. Or a mother's look, a comforting word from a friend, timely attention.
Physicists mean by this a very specific term. And very important, especially in some sections of this complex but fascinating science.
Thermodynamics
It is not worth considering the amount of heat in isolation from the simplest processes on which the law of conservation of energy is based - nothing will be clear. Therefore, to begin with, we remind our readers.
Thermodynamics considers any thing or object as a combination of a very large number of elementary parts - atoms, ions, molecules. Its equations describe any change in the collective state of the system as a whole and as part of the whole when changing macro parameters. The latter are understood as temperature (denoted as T), pressure (P), concentration of components (usually C).
Internal energy
Internal energy is a rather complicated term, the meaning of which should be understood before talking about the amount of heat. It denotes the energy that changes with an increase or decrease in the value of the object's macro parameters and does not depend on the reference system. It is part of the total energy. It coincides with it under conditions when the center of mass of the thing under study is at rest (that is, there is no kinetic component).
When a person feels that some object (say, a bicycle) has warmed up or cooled down, this shows that all the molecules and atoms that make up this system have experienced a change in internal energy. However, the constancy of temperature does not mean the preservation of this indicator.
Work and warmth
The internal energy of any thermodynamic system can be transformed in two ways:
- by doing work on it;
- during heat exchange with the environment.
The formula for this process looks like this:
dU=Q-A, where U is internal energy, Q is heat, A is work.
Let the reader not be deceived by the simplicity of the expression. The permutation shows that Q=dU+A, but the introduction of entropy (S) brings the formula to the form dQ=dSxT.
Since in this case the equation takes the form of a differential equation, the first expression requires the same. Further, depending on the forces acting in the object under study and the parameter that is being calculated, the necessary ratio is derived.
Let us take a metal ball as an example of a thermodynamic system. If you put pressure on it, throw it up, drop it into a deep well, then this means doing work on it. Outwardly, all these harmless actions will not cause any harm to the ball, but its internal energy will change, albeit very slightly.
The second way is heat transfer. Now we come to the main goal of this article: a description of what the amount of heat is. This is such a change in the internal energy of a thermodynamic system that occurs during heat transfer (see the formula above). It is measured in joules or calories. Obviously, if the ball is held over a lighter, in the sun, or simply in a warm hand, it will heat up. And then, by changing the temperature, you can find the amount of heat that was communicated to him at the same time.
Why gas is the best example of a change in internal energy, and why students don't like physics because of it
Above, we described changes in the thermodynamic parameters of a metal ball. They are not very noticeable without special devices, and the reader is left to take a word about the processes occurring with the object. Another thing is if the system is gas. Press on it - it will be visible, heat it up - the pressure will rise, lower it underground - and this can be easily fixed. Therefore, in textbooks, it is gas that is most often taken as a visual thermodynamic system.
But, alas, not much attention is paid to real experiments in modern education. A scientist who writes a methodological manual understands perfectly well what is at stake. It seems to him that, using the example of gas molecules, all thermodynamic parameters will be adequately demonstrated. But for a student who is just discovering this world, it is boring to hear about an ideal flask with a theoretical piston. If the school had real research laboratories and dedicated hours to work in them, everything would be different. So far, unfortunately, the experiments are only on paper. And, most likely, this is precisely what causes people to consider this branch of physics as something purely theoretical, far from life and unnecessary.
Therefore, we decided to give the bicycle already mentioned above as an example. A person presses on the pedals - does work on them. In addition to communicating torque to the entire mechanism (due to which the bicycle moves in space), the internal energy of the materials from which the levers are made changes. The cyclist pushes the handles to turn, and again does the work.
The internal energy of the outer coating (plastic or metal) is increased. A person goes to a clearing under the bright sun - the bike heats up, its amount of heat changes. Stops to rest in the shade of an old oak tree and the system cools down, wasting calories or joules. Increases speed - increases the exchange of energy. However, the calculation of the amount of heat in all these cases will show a very small, imperceptible value. Therefore, it seems that there are no manifestations of thermodynamic physics in real life.
Application of calculations for changes in the amount of heat
Probably, the reader will say that all this is very informative, but why are we so tortured at school with these formulas. And now we will give examples in which areas of human activity they are directly needed and how this applies to anyone in his everyday life.
To begin with, look around you and count: how many metal objects surround you? Probably more than ten. But before becoming a paper clip, wagon, ring or flash drive, any metal is smelted. Every plant that processes, say, iron ore must understand how much fuel is required in order to optimize costs. And when calculating this, it is necessary to know the heat capacity of the metal-containing raw materials and the amount of heat that must be imparted to it in order for all technological processes to take place. Since the energy released by a unit of fuel is calculated in joules or calories, the formulas are needed directly.
Or another example: most supermarkets have a department with frozen goods - fish, meat, fruits. Where raw materials from animal meat or seafood are converted into semi-finished products, they must know how much electricity refrigeration and freezing units will use per ton or unit of finished product. To do this, you should calculate how much heat a kilogram of strawberries or squids loses when cooled by one degree Celsius. And in the end, this will show how much electricity a freezer of a certain capacity will spend.
Planes, ships, trains
Above, we have shown examples of relatively immobile, static objects that are informed or, on the contrary, a certain amount of heat is taken away from them. For objects moving in the process of operation in conditions of constantly changing temperature, calculations of the amount of heat are important for another reason.
There is such a thing as "metal fatigue". It also includes the maximum allowable loads at a certain rate of temperature change. Imagine an airplane taking off from the humid tropics into the frozen upper atmosphere. Engineers have to work hard so that it does not fall apart due to cracks in the metal that appear when the temperature changes. They are looking for an alloy composition that can withstand real loads and will have a large margin of safety. And in order not to search blindly, hoping to accidentally stumble upon the desired composition, you have to do a lot of calculations, including those that include changes in the amount of heat.
HEAT EXCHANGE.
1.Heat transfer.
Heat exchange or heat transfer is the process of transferring the internal energy of one body to another without doing work.
There are three types of heat transfer.
1) Thermal conductivity is the heat exchange between bodies in direct contact.
2) Convection is heat transfer in which heat is transferred by gas or liquid flows.
3) Radiation is heat transfer by means of electromagnetic radiation.
2. The amount of heat.
The amount of heat is a measure of the change in the internal energy of a body during heat exchange. Denoted by letter Q.
The unit of measurement of the amount of heat = 1 J.
The amount of heat received by a body from another body as a result of heat transfer can be spent on increasing the temperature (increasing the kinetic energy of molecules) or on changing the state of aggregation (increasing potential energy).
3. Specific heat capacity of a substance.
Experience shows that the amount of heat required to heat a body of mass m from temperature T 1 to temperature T 2 is proportional to the body mass m and the temperature difference (T 2 - T 1), i.e.
Q = cm(T 2 - T 1 ) = withmΔ T,
With is called the specific heat capacity of the substance of the heated body.
The specific heat capacity of a substance is equal to the amount of heat that must be imparted to 1 kg of the substance in order to heat it by 1 K.
Unit of specific heat capacity =.
The heat capacity values of various substances can be found in physical tables.
Exactly the same amount of heat Q will be released when the body is cooled by ΔT.
4. Specific heat of vaporization.
Experience shows that the amount of heat required to convert a liquid into vapor is proportional to the mass of the liquid, i.e.
Q = lm,
where is the coefficient of proportionality L is called the specific heat of vaporization.
The specific heat of vaporization is equal to the amount of heat that is necessary to convert 1 kg of liquid at the boiling point into steam.
Unit of measure for the specific heat of vaporization.
In the reverse process, the condensation of steam, heat is released in the same amount that was spent on vaporization.
5. Specific heat of fusion.
Experience shows that the amount of heat required to transform a solid into a liquid is proportional to the mass of the body, i.e.
Q = λ m,
where the coefficient of proportionality λ is called the specific heat of fusion.
The specific heat of fusion is equal to the amount of heat that is necessary to turn a solid body weighing 1 kg into a liquid at the melting point.
Unit of measure for specific heat of fusion.
In the reverse process, the crystallization of a liquid, heat is released in the same amount that was spent on melting.
6. Specific heat of combustion.
Experience shows that the amount of heat released during the complete combustion of the fuel is proportional to the mass of the fuel, i.e.
Q = qm,
Where the proportionality factor q is called the specific heat of combustion.
The specific heat of combustion is equal to the amount of heat that is released during the complete combustion of 1 kg of fuel.
Unit of measure for specific heat of combustion.
7. Heat balance equation.
Two or more bodies are involved in heat exchange. Some bodies give off heat, while others receive it. Heat transfer occurs until the temperatures of the bodies become equal. According to the law of conservation of energy, the amount of heat that is given off is equal to the amount that is received. On this basis, the heat balance equation is written.
Consider an example.
A body of mass m 1 , whose heat capacity is c 1 , has temperature T 1 , and a body of mass m 2 , whose heat capacity is c 2 , has temperature T 2 . Moreover, T 1 is greater than T 2. These bodies are brought into contact. Experience shows that a cold body (m 2) begins to heat up, and a hot body (m 1) begins to cool. This suggests that part of the internal energy of a hot body is transferred to a cold one, and the temperatures even out. Let us denote the final total temperature by θ. 
The amount of heat transferred from a hot body to a cold one
Q transferred. = c 1 m 1 (T 1 – θ )
The amount of heat received by a cold body from a hot one
Q received. = c 2 m 2 (θ – T 2 )
According to the law of conservation of energy Q transferred. = Q received., i.e.
c 1 m 1 (T 1 – θ )= c 2 m 2 (θ – T 2 )
Let us open the brackets and express the value of the total steady-state temperature θ.
The temperature value θ in this case will be obtained in kelvins.
However, since in the expressions for Q passed. and Q is received. if there is a difference between two temperatures, and it is the same in both kelvins and degrees Celsius, then the calculation can be carried out in degrees Celsius. Then
In this case, the temperature value θ will be obtained in degrees Celsius.
The alignment of temperatures as a result of heat conduction can be explained on the basis of molecular kinetic theory as the exchange of kinetic energy between molecules during collision in the process of thermal chaotic motion.
This example can be illustrated with a graph. 
