Quantity of heat. Heat units. Specific heat. Calculation of the amount of heat required to heat the body or released by it during cooling. Calculation of the amount of heat during heat transfer, specific heat capacity of a substance. Equation those

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 the piston is fixed, then the volume of the gas will not change, but the temperature, and hence the internal energy, will increase.
The process of transferring energy from one body to another without doing work is called heat transfer or heat transfer.

The energy transferred to the body as a result of heat transfer is called the amount of heat. The amount of heat is also called the energy that the body gives off in the process of heat transfer.

Molecular picture of heat transfer. During heat exchange at the boundary between bodies, slowly moving molecules of a cold body interact with faster 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 hot body is transferred to a cold body.

The amount of heat and heat capacity. It is known from the class VII physics course that in order to heat a body with mass m from temperature t 1 to temperature t 2, it is necessary to inform it of the amount of heat

Q \u003d cm (t 2 - t 1) \u003d cmΔt. (4.5)

When a body cools, its eternal temperature t 2 is less than the initial 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. Specific heat capacity is the amount of heat that 1 kg of a substance receives or gives off when its temperature changes by 1 K.

Specific heat capacity is expressed in joules per kilogram times kelvin. Different bodies require a different amount of energy to increase the 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).

The specific heat capacity depends not only on the properties of the substance, but also on the process by which heat transfer takes place. 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 will need to transfer more heat than to heat it at constant volume.

Liquids and solids expand slightly when heated, and their specific heat capacities at constant volume and constant pressure differ little.

Specific heat of vaporization. To convert a liquid into vapor, a certain amount of heat must be transferred to it. The temperature of the liquid does not change during this transformation. 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 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 the forces of external pressure.

The amount of heat required to convert 1 kg of liquid to vapor at a constant temperature is called the specific heat of vaporization. This value 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 100°C. For other liquids (alcohol, ether, mercury, kerosene, etc.), the specific heat of vaporization is 3-10 times less.

To convert a liquid of mass m into vapor requires an amount of heat equal to:

When steam condenses, the same amount of heat is released

Qk = –rm. (4.7)

The amount of heat λ (lambda) required to convert 1 kg of a crystalline substance at a melting point into a liquid of the same temperature is called the specific heat of fusion.

During the crystallization of 1 kg of a substance, exactly the same amount of heat is released. The specific heat of ice melting is rather 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 \u003d λm. (4.8)

The amount of heat released during the crystallization of the body is equal to:

Q cr = - λm. (4.9)

1. What is called the amount of heat? 2. What determines the specific heat capacity of substances? 3. What is called the specific heat of vaporization? 4. What is called the specific heat of fusion? 5. In what cases is the amount of transferred heat negative?

In this lesson, we will learn how to calculate the amount of heat needed to heat a body or release it when it cools. To do this, we will summarize the knowledge that was obtained in previous lessons.

In addition, we will learn how to use 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 by it when cooled.

The ability to calculate the required amount of heat is very important. This may be necessary, for example, when calculating the amount of heat that must be imparted to water to heat a room.

Rice. 1. The amount of heat that must be reported 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

Also, this knowledge is needed, for example, to determine the amount of heat that is released by the Sun and hits 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 with a scale);
the temperature difference by which it is necessary to heat the body or cool it (usually measured with 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 for calculating the amount of heat is as follows:

This formula contains the following quantities:

The amount of heat, measured in joules (J);

The specific heat capacity of a substance, measured in;

- temperature difference, measured in degrees Celsius ().

Consider the problem of calculating the amount of heat.

A task

A copper glass with a mass of grams contains water with a volume of one liter at a temperature of . How much heat must be transferred to a glass of water so that its temperature becomes equal to ?

Rice. 5. Illustration of the condition of the problem

First, we write a short condition ( Given) and convert all quantities to the international system (SI).

*Given:*	SI

*Find:*

Solution:

First, determine what other quantities we need to solve this problem. According to 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 in order to calculate the amount of heat, we need a mass of water. By condition, we are given only the volume. Therefore, we take the density of water from the table: (Table 2).

Tab. 1. Specific heat capacity of some substances,

Tab. 2. Densities of some liquids

Now we have everything we need to solve this problem.

Note that the total 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:

We first calculate the amount of heat required to heat the copper glass:

Before calculating the amount of heat required to heat water, we calculate the mass of water using the formula familiar to us from grade 7:

Now we can calculate:

Then we can calculate:

Recall what it means: kilojoules. The prefix "kilo" means .

Answer:.

For the convenience of solving problems of finding the amount of heat (the so-called direct problems) and the quantities associated with this concept, you can use the following table.

Desired value	Designation	Units	Basic Formula	Formula for quantity
Quantity of heat

The process of transferring energy from one body to another without doing work is called heat transfer or heat transfer.

The energy transferred to the body as a result of heat transfer is called the amount of heat. The amount of heat is also called the energy that the body gives off in the process of heat transfer.

molecules are aligned and the velocities of the molecules of a cold body increase, and those of a hot one decrease.

During heat exchange, there is no conversion of energy from one form to another: part of the internal energy of a hot body is transferred to a cold body.

The amount of heat and heat capacity. From the class VII physics course, it is known that in order to heat a body with a mass from temperature to temperature, it is necessary to inform it of the amount of heat

When the body cools, its final temperature is less than the initial one and the amount of heat given off by the body is negative.

The coefficient c in formula (4.5) is called the specific heat capacity. Specific heat capacity is the amount of heat that 1 kg of a substance receives or gives off when its temperature changes by 1 K -

Specific heat capacity is expressed in joules per kilogram times kelvin. Different bodies require an unequal amount of energy to increase the temperature by I K. Thus, the specific heat capacity of water and copper

The specific heat capacity depends not only on the properties of the substance, but also on the process in which heat transfer takes place. 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 will need to transfer more heat than to heat it at constant volume.

Liquids and solids expand slightly when heated, and their specific heat capacities at constant volume and constant pressure differ little.

Specific heat of vaporization. To convert a liquid into vapor, a certain amount of heat must be transferred to it. The temperature of the liquid does not change during this transformation. 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 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 performed against the forces of external pressure.

The amount of heat required to turn 1 kg of liquid into vapor at a constant temperature is called

specific heat of vaporization. This value is denoted by a letter and expressed in joules per kilogram.

The specific heat of vaporization of water is very high: 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 convert a liquid mass into vapor requires an amount of heat equal to:

When steam condenses, the same amount of heat is released:

The amount of heat A required to convert 1 kg of a crystalline substance at the melting point into a liquid of the same temperature is called the specific heat of fusion.

During the crystallization of 1 kg of a substance, exactly the same amount of heat is released. The specific heat of melting of ice is quite high:

In order to melt a crystalline body with a mass, an amount of heat is required equal to:

The amount of heat released during the crystallization of the body is equal to:

>>Physics: Quantity of heat

It is possible to change the internal energy of the gas in the cylinder not only by doing work, but also by heating the gas.
If you fix the piston ( fig.13.5), then the volume of the gas does not change when heated and no work is done. But the temperature of the gas, and hence its internal energy, increases.

The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer.
The quantitative measure of the change in internal energy during heat transfer is called amount of heat. The amount of heat is also called the energy that the body gives off in the process of heat transfer.
Molecular picture of heat transfer
During heat exchange, there is no conversion of energy from one form to another; part of the internal energy of a hot body is transferred to a cold body.
The amount of heat and heat capacity. You already know that to heat a body with a mass m temperature t1 up to temperature t2 it is necessary to transfer the amount of heat to it:

When a body cools, its final temperature t2 is less than the initial temperature t1 and the amount of heat given off by the body is negative.
Coefficient c in formula (13.5) is called specific heat substances. Specific heat capacity is a value numerically equal to the amount of heat that a 1 kg substance receives or gives off when its temperature changes by 1 K.
The specific heat capacity depends not only on the properties of the substance, but also on the process by which heat transfer takes place. 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 a 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. 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: rH2O\u003d 2.256 10 6 J / kg at a temperature of 100 ° C. In other liquids, for example, alcohol, ether, mercury, kerosene, the specific heat of vaporization is 3-10 times less than that of water.
To transform a liquid into a mass m steam requires an amount of heat equal to:

When steam condenses, the same amount of heat is released:

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.
A value numerically equal to the amount of heat required to convert a crystalline substance weighing 1 kg at a melting point into a liquid is called specific heat of fusion.
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,” wrote R. Black back in the 18th century, “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.”
In order to melt a crystalline body with a mass m, the amount of heat required is:

The amount of heat released during the crystallization of the body is equal to:

The internal energy of a body changes during heating and cooling, during vaporization and condensation, during melting and crystallization. In all cases, a certain amount of heat is transferred to or removed from the body.

???
1. What is called quantity warmth?
2. What does the specific heat capacity of a substance depend on?
3. What is called the specific heat of vaporization?
4. What is called the specific heat of fusion?
5. In what cases is the amount of heat a positive value, and in what cases is it negative?

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics Grade 10

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The internal energy of the body can change due to the work of external forces. To characterize the change in internal energy during heat transfer, a quantity called the amount of heat and denoted by Q is introduced.

In the international system, the unit of the amount of heat, as well as work and energy, is the joule: = = = 1 J.

In practice, an off-system unit of the amount of heat is sometimes used - a calorie. 1 cal. = 4.2 J.

It should be noted that the term "quantity of heat" is unfortunate. It was introduced at a time when it was believed that bodies contained some weightless, elusive liquid - caloric. The process of heat transfer allegedly consists in the fact that caloric, pouring from one body into another, carries with it a certain amount of heat. Now, knowing the basics of the molecular-kinetic theory of the structure of matter, we understand that there is no caloric in bodies, the mechanism for changing the internal energy of a body is different. However, the power of tradition is great and we continue to use the term, introduced on the basis of incorrect ideas about the nature of heat. At the same time, understanding the nature of heat transfer, one should not completely ignore misconceptions about it. On the contrary, by drawing an analogy between the flow of heat and the flow of a hypothetical liquid of caloric, the amount of heat and the amount of caloric, it is possible, when solving some classes of problems, to visualize the ongoing processes and solve problems correctly. In the end, the correct equations describing the processes of heat transfer were obtained at one time on the basis of incorrect ideas about caloric as a heat carrier.

Let us consider in more detail the processes that can occur as a result of heat transfer.

Pour some water into a test tube and close it with a cork. Hang the test tube to a rod fixed in a tripod and bring an open flame under it. From the flame, the test tube receives a certain amount of heat and the temperature of the liquid in it rises. As the temperature rises, the internal energy of the liquid increases. There is an intensive process of its vaporization. The expanding liquid vapors do mechanical work to push the stopper out of the tube.

Let's conduct another experiment with a model of a cannon made from a piece of brass tube, which is mounted on a trolley. On one side, the tube is tightly closed with an ebonite plug, through which a pin is passed. Wires are soldered to the stud and tube, ending in terminals that can be energized from the lighting network. The gun model is thus a kind of electric boiler.

Pour some water into the cannon barrel and close the tube with a rubber stopper. Connect the gun to a power source. An electric current passing through water heats it up. Water boils, which leads to its intense vaporization. The pressure of water vapor increases and, finally, they do the work of pushing the cork out of the gun barrel.

The gun, due to recoil, rolls back in the direction opposite to the cork launch.

Both experiences are united by the following circumstances. In the process of heating the liquid in various ways, the temperature of the liquid and, accordingly, its internal energy increased. In order for the liquid to boil and evaporate intensively, it was necessary to continue heating it.

The vapors of the liquid, due to their internal energy, performed mechanical work.

We investigate the dependence of the amount of heat necessary to heat the body on its mass, temperature changes and the type of substance. To study these dependencies, we will use water and oil. (To measure the temperature in the experiment, an electric thermometer is used, made of a thermocouple connected to a mirror galvanometer. One thermocouple junction is lowered into a vessel with cold water to ensure its temperature is constant. The other thermocouple junction measures the temperature of the liquid under study).

The experience consists of three series. In the first series, for a constant mass of a particular liquid (in our case, water), the dependence of the amount of heat required to heat it on temperature changes is studied. The amount of heat received by the liquid from the heater (electric stove) will be judged by the heating time, assuming that there is a directly proportional relationship between them. In order for the result of the experiment to correspond to this assumption, it is necessary to ensure a steady flow of heat from the electric stove to the heated body. To do this, the electric stove was connected to the network in advance, so that by the beginning of the experiment the temperature of its surface would cease to change. For more uniform heating of the liquid during the experiment, we will stir it with the help of the thermocouple itself. We will record the readings of the thermometer at regular intervals until the light spot reaches the edge of the scale.

Let us conclude: there is a direct proportional relationship between the amount of heat required to heat a body and a change in its temperature.

In the second series of experiments, we will compare the amount of heat required to heat the same liquids of different masses when their temperature changes by the same amount.

For the convenience of comparing the obtained values, the mass of water for the second experiment will be taken two times less than in the first experiment.

Again, we will record the thermometer readings at regular intervals.

Comparing the results of the first and second experiments, we can draw the following conclusions.

In the third series of experiments, we will compare the amounts of heat required to heat equal masses of different liquids when their temperature changes by the same amount.

We will heat oil on an electric stove, the mass of which is equal to the mass of water in the first experiment. We will record the thermometer readings at regular intervals.

The result of the experiment confirms the conclusion that the amount of heat necessary to heat the body is directly proportional to the change in its temperature and, in addition, indicates the dependence of this amount of heat on the type of substance.

Since oil was used in the experiment, the density of which is less than the density of water, and a smaller amount of heat was required to heat the oil to a certain temperature than to heat water, it can be assumed that the amount of heat required to heat the body depends on its density.

To test this assumption, we will simultaneously heat identical masses of water, paraffin and copper on a heater of constant power.

After the same time, the temperature of copper is about 10 times, and paraffin is about 2 times higher than the temperature of water.

But copper has a greater and paraffin less density than water.

Experience shows that the quantity that characterizes the rate of change in the temperature of the substances from which the bodies involved in heat exchange are made is not the density. This quantity is called the specific heat capacity of the substance and is denoted by the letter c.

A special device is used to compare the specific heat capacities of various substances. The device consists of racks in which a thin paraffin plate and a bar with rods passed through it are attached. Aluminum, steel and brass cylinders of equal mass are fixed at the ends of the rods.

We heat the cylinders to the same temperature by immersing them in a vessel of water standing on a hot electric stove. Let's fix the hot cylinders on the racks and release them from the fasteners. The cylinders simultaneously touch the paraffin plate and, melting the paraffin, begin to sink into it. The depth of immersion of cylinders of the same mass into a paraffin plate, when their temperature changes by the same amount, turns out to be different.

Experience shows that the specific heat capacities of aluminum, steel and brass are different.

Having done the corresponding experiments with the melting of solids, the vaporization of liquids, and the combustion of fuel, we obtain the following quantitative dependences.

To obtain units of specific quantities, they must be expressed from the corresponding formulas and the units of heat - 1 J, mass - 1 kg, and for specific heat - and 1 K should be substituted into the resulting expressions.

We get units: specific heat capacity - 1 J / kg K, other specific heats: 1 J / kg.