The concept of the amount of heat was formed in the early stages of the development of modern physics, when there were no clear ideas about the internal structure of matter, what energy is, what forms of energy exist in nature and about energy as a form of movement and transformation of matter.
The amount of heat is understood as a physical quantity equivalent to the energy transferred to a material body in the process of heat exchange.
The outdated unit of heat is the calorie, equal to 4.2 J; today this unit is practically not used, and the joule has taken its place.
Initially, it was assumed that the carrier of thermal energy was some completely weightless medium with the properties of a liquid. Numerous physical problems of heat transfer have been and are still being solved based on this premise. The existence of hypothetical caloric was the basis for many essentially correct constructions. It was believed that caloric is released and absorbed in the phenomena of heating and cooling, melting and crystallization. The correct equations for heat transfer processes were obtained based on incorrect physical concepts. There is a known law according to which the amount of heat is directly proportional to the mass of the body participating in heat exchange and the temperature gradient:
Where Q is the amount of heat, m is the body mass, and the coefficient With– a quantity called specific heat capacity. Specific heat capacity is a characteristic of a substance involved in a process.
Work in thermodynamics
As a result of thermal processes, purely mechanical work can be performed. For example, when a gas heats up, it increases its volume. Let's take a situation like the picture below:
In this case, the mechanical work will be equal to the force of gas pressure on the piston multiplied by the path traveled by the piston under pressure. Of course, this is the simplest case. But even in it one can notice one difficulty: the pressure force will depend on the volume of the gas, which means that we are not dealing with constants, but with variable quantities. Since all three variables: pressure, temperature and volume are related to each other, calculating work becomes significantly more complicated. There are some ideal, infinitely slow processes: isobaric, isothermal, adiabatic and isochoric - for which such calculations can be performed relatively simply. A graph of pressure versus volume is plotted and the work is calculated as an integral of the form.
« Physics - 10th grade"
In what processes do aggregate transformations of matter occur?
How can you change the state of aggregation of a substance?
You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
So, when forging a metal, work is done and it heats up, 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 therefore 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, the interaction of slowly moving molecules of a cold body with fast moving molecules of a hot body occurs. As a result, the kinetic energies of the molecules are equalized and the speeds of the molecules of a cold body increase, and those of a hot body decrease.
During heat exchange, energy is not converted from one form to another; part of the internal energy of a more heated body is transferred to a less heated body.
Amount of heat and heat capacity.
You already know that to heat a body of mass m from temperature t 1 to temperature t 2 it is necessary to transfer an amount of heat to it:
Q = cm(t 2 - t 1) = cm Δt. (13.5)
When a 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 quantity numerically equal to the amount of heat that a substance weighing 1 kg receives or releases when its temperature changes by 1 K.
The specific heat capacity of gases depends on the process by which heat transfer occurs. 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 transform a liquid into steam during the boiling process, a certain amount of heat must be transferred to it. The temperature of a liquid does not change when it boils. The transformation of a liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of the 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.
A quantity numerically equal to the amount of heat required to convert a liquid weighing 1 kg into steam at a constant temperature is called specific heat of vaporization.
The process of evaporation of a liquid occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of evaporation is equal to the specific heat of vaporization.
This value is denoted by the letter r and 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. For other liquids, for example 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 vapor, an amount of heat is required equal to:
Q p = rm. (13.6)
When steam condenses, the same amount of heat is released:
Q k = -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 between molecules. The kinetic energy of the molecules does not change, since melting occurs at a constant temperature.
A value numerically equal to the amount of heat required to transform a crystalline substance weighing 1 kg at the melting point into a liquid is called specific heat of fusion and are denoted by the letter λ.
When a substance weighing 1 kg crystallizes, exactly the same amount of heat is released as is absorbed during melting.
The specific heat of melting of ice is quite high: 3.34 10 5 J/kg.
“If ice did not have a high heat of fusion, then in the spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to the ice from the air. The consequences of this would be dire; after all, even in the current situation, large floods and strong flows of water arise when large masses of ice or snow melt.” R. Black, XVIII century.
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl = λm. (13.8)
The amount of heat released during crystallization of a body is equal to:
Q cr = -λm (13.9)
Heat balance equation.
Let us consider the heat exchange within a system consisting of several bodies that initially have different temperatures, for example, the heat exchange between water in a vessel and a hot iron ball lowered into the 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 amount of heat given is considered negative, the amount of heat received 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 are the amounts of heat received or given off by bodies. These amounts of heat are expressed by formula (13.5) or formulas (13.6)-(13.9), if various phase transformations of the substance (melting, crystallization, vaporization, condensation) occur during the heat exchange process.
In this lesson we will learn how to calculate the amount of heat required to heat a body or released by it when cooling. To do this, we will summarize the knowledge that was acquired in previous lessons.
In addition, we will learn, using the formula for the amount of heat, to express the remaining quantities from this formula and calculate them, knowing other quantities. An example of a problem with a solution for calculating the amount of heat will also be considered.
This lesson is devoted to calculating the amount of heat when a body is heated or released when cooled.
The ability to calculate the required amount of heat is very important. This may be needed, for example, when calculating the amount of heat that needs to be imparted to water to heat a room.
Rice. 1. The amount of heat that must be imparted to the water to heat the room
Or to calculate the amount of heat that is released when fuel is burned in various engines:
Rice. 2. The amount of heat that is released when fuel is burned in the engine
This knowledge is also needed, for example, to determine the amount of heat that is released by the Sun and falls on the Earth:
Rice. 3. The amount of heat released by the Sun and falling on the Earth
To calculate the amount of heat, you need to know three things (Fig. 4):
- body weight (which can usually be measured using a scale);
- the temperature difference by which a body must be heated or cooled (usually measured using a thermometer);
- specific heat capacity of the body (which can be determined from the table).
Rice. 4. What you need to know to determine
The formula by which the amount of heat is calculated looks like this:
The following quantities appear in this formula:
The amount of heat measured in joules (J);
The specific heat capacity of a substance is measured in ;
- temperature difference, measured in degrees Celsius ().
Let's consider the problem of calculating the amount of heat.
Task
A copper glass with a mass of grams contains water with a volume of liter at a temperature. How much heat must be transferred to a glass of water so that its temperature becomes equal to ?
Rice. 5. Illustration of the problem conditions
First we write down a short condition ( Given) and convert all quantities to the international system (SI).
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Given: |
SI |
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Find: |
Solution:
First, determine what other quantities we need to solve this problem. Using the table of specific heat capacity (Table 1) we find (specific heat capacity of copper, since by condition the glass is copper), (specific heat capacity of water, since by condition there is water in the glass). In addition, we know that to calculate the amount of heat we need a mass of water. According to the condition, we are given only the volume. Therefore, from the table we take the density of water: (Table 2).
Table 1. Specific heat capacity of some substances,
Table 2. Densities of some liquids
Now we have everything we need to solve this problem.
Note that the final amount of heat will consist of the sum of the amount of heat required to heat the copper glass and the amount of heat required to heat the water in it:
Let's first calculate the amount of heat required to heat a copper glass:
Before calculating the amount of heat required to heat water, let’s calculate the mass of water using a formula that is familiar to us from grade 7:
Now we can calculate:
Then we can calculate:
Let's remember what kilojoules mean. The prefix "kilo" means 
.
Answer:.
For the convenience of solving problems of finding the amount of heat (the so-called direct problems) and quantities associated with this concept, you can use the following table.
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Required quantity |
Designation |
Units of measurement |
Basic formula |
Formula for quantity |
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Amount of heat |
The internal energy of a thermodynamic system can be changed in two ways:
- doing work on the system,
- using thermal interaction.
The transfer of heat to a body is not associated 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 a body with a higher temperature do work on some molecules of a body that has a lower temperature. In this case, thermal interaction is realized due to thermal conductivity. Energy transfer is also possible using radiation. The system of microscopic processes (relating 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 refers to the energy that is received (or given up) by a body in the process of heat exchange with surrounding bodies (environment). The symbol for heat is usually 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 transferred to the system (body), or it can be taken from it. It is believed that if heat is transferred to the system, then it is positive.
Formula for calculating heat when temperature changes
We denote the elementary amount of heat as . Let us note that the element of heat that the system receives (gives) with a small change in its state is not a complete 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 imparted to the system, and the temperature changes from T to T+dT, is equal to:
where C is the heat capacity of the body. If the body in question is homogeneous, then formula (1) for the amount of heat can be represented as:
where is the specific heat capacity 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 an amount can be calculated as:
where t 2, t 1 body temperature before and after heating. Please note that when finding the difference () in calculations, temperatures can be substituted both in degrees Celsius and in kelvins.
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 phase transition.
Thus, to transfer an element of matter from the state of a solid to a liquid, it should be given an amount of heat () equal to:
where is the specific heat of fusion, dm is the element of body mass. 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 evaporation) required to convert liquid into vapor can be found as:
where r is the specific heat of evaporation. When steam condenses, heat is released. The heat of evaporation is equal to the heat of condensation of equal masses of substance.
Units for measuring the amount of heat
The basic unit of measurement for the amount of heat in the SI system is: [Q]=J
An extra-system unit of heat, which 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 = 10 C, the temperature of the second mass of water is t 2 = 60 C?
Solution. Let us write the heat balance equation in the form:
where Q=cmt is the amount of heat prepared after mixing the water; Q 1 = cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 = cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.
From equation (1.1) it follows:
When combining cold (V 1) and hot (V 2) parts of water into a single volume (V), we can assume that:
So, we get a system of equations:
Having solved it we get:
You can change the internal energy of the gas in the cylinder not only by doing work, but also by heating the gas (Fig. 43). If you fix the piston, the volume of the gas will not change, but the temperature, and therefore the internal energy, will increase.
The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer.
The energy transferred to the body as a result of heat exchange is called the amount of heat. The amount of heat is also called the energy that a body gives off during heat exchange.
Molecular picture of heat transfer. During heat exchange at the boundary between bodies, the interaction of slowly moving molecules of a cold body with faster moving molecules of a hot body occurs. As a result, the kinetic energies of the molecules are equalized and the speeds of the molecules of a cold body increase, and those of a hot body decrease.
During heat exchange, energy is not converted from one form to another: part of the internal energy of a hot body is transferred to a cold body.
Amount of heat and heat capacity. From the VII class physics course it is known that in order to heat a body of mass m from temperature t 1 to temperature t 2 it is necessary to inform it of the amount of heat
Q = cm(t 2 – t 1) = cmΔt. (4.5)
When a body cools, its eternal temperature t 2 is less than the initial temperature t 1 and the amount of heat given off by the body is negative.
The coefficient c in formula (4.5) is called specific heat capacity. Specific heat capacity is the amount of heat that 1 kg of a substance receives or releases when its temperature changes by 1 K.
Specific heat capacity is expressed in joules divided by kilogram multiplied by kelvin. Different bodies require different amounts of energy to increase temperature by 1 K. Thus, the specific heat capacity of water is 4190 J/(kg K), and that of copper is 380 J/(kg K).
Specific heat capacity depends not only on the properties of the substance, but also on the process by which heat transfer occurs. If you heat a gas at constant pressure, it will expand and do work. To heat a gas by 1°C at constant pressure, more heat will need to be transferred to it than to heat it at constant volume.
Liquid and solid bodies expand slightly when heated, and their specific heat capacities at constant volume and constant pressure differ little.
Specific heat of vaporization. To transform a liquid into steam, a certain amount of heat must be transferred to it. The temperature of the liquid does not change during this transformation. The transformation of a liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of the molecules, but is accompanied by an increase in their potential energy. After all, the average distance between gas molecules is many times greater than between liquid molecules. In addition, an increase in volume during the transition of a substance from a liquid to a gaseous state requires work to be done against external pressure forces.
The amount of heat required to convert 1 kg of liquid into steam at a constant temperature is called the specific heat of vaporization. This quantity is denoted by the letter r and expressed in joules per kilogram.
The specific heat of vaporization of water is very high: 2.256 · 10 6 J/kg at a temperature of 100°C. For other liquids (alcohol, ether, mercury, kerosene, etc.) the specific heat of vaporization is 3-10 times less.
To transform a liquid of mass m into vapor, an amount of heat is required equal to:
When steam condenses, the same amount of heat is released
Q k = –rm. (4.7)
Specific heat of fusion. When a crystalline body melts, all the heat supplied to it goes to increase the potential energy of the molecules. The kinetic energy of the molecules does not change, since melting occurs at a constant temperature.
The amount of heat λ (lambda) required to convert 1 kg of a crystalline substance at the melting point into a liquid at the same temperature is called the specific heat of fusion.
When 1 kg of a substance crystallizes, exactly the same amount of heat is released. The specific heat of melting of ice is quite high: 3.4 · 10 5 J/kg.
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl = λm. (4.8)
The amount of heat released during crystallization of a body is equal to:
Qcr = – λm. (4.9)
1. What is the amount of heat called? 2. What does the specific heat capacity of substances depend on? 3. What is called the specific heat of vaporization? 4. What is the specific heat of fusion called? 5. In what cases is the amount of heat transferred negative?
