What formula is used to calculate the amount of heat received. The amount of heat, specific heat capacity

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 international system the unit of heat quantity, 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. Electricity, passing through the water, heats it. 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. During the heating of the liquid different 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 junction of the thermocouple is lowered into a vessel with cold water to keep its temperature constant. The other junction of the thermocouple measures the temperature of the test liquid.)

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. We will judge the amount of heat received by the liquid from the heater (electric stove) by the heating time, assuming that there is a direct relationship between them. proportional dependence. 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.

The internal energy of a body depends on its temperature and external conditions - volume, etc. If external conditions remain unchanged, i.e., the volume and other parameters are constant, then the internal energy of the body depends only on its temperature.

It is possible to change the internal energy of a body not only by heating it in a flame or by performing mechanical work on it (without changing the position of the body, for example, the work of the friction force), but also by bringing it into contact with another body that has a temperature different from the temperature given body, i.e., through heat transfer.

The amount of internal energy that a body gains or loses in the process of heat transfer is called the “amount of heat”. The amount of heat is usually denoted by the letter `Q`. If the internal energy of the body in the process of heat transfer increases, then the heat is assigned a plus sign, and the body is said to have been given heat `Q`. With a decrease in internal energy in the process of heat transfer, heat is considered negative, and it is said that the amount of heat `Q` has been taken (or removed) from the body.

The amount of heat can be measured in the same units in which mechanical energy is measured. In SI it is `1` joule. There is another unit of heat measurement - calorie. Calorie is the amount of heat required to heat `1` g of water by `1^@ bb"C"`. The ratio between these units was established by Joule: `1` cal `= 4.18` J. This means that due to work in `4.18` kJ, the temperature of `1` kilogram of water will increase by `1` degree.

The amount of heat required to heat the body by `1^@ bb"C"` is called the heat capacity of the body. The heat capacity of a body is denoted by the letter `C`. If the body was told a small amount of heat `Delta Q`, and body temperature has changed by `Delta t` degrees, then

`Q=C*Deltat=C*(t_2 - t_1)=c*m*(t_2 - t_1)`.

(1.3)

If the body is surrounded by a shell that conducts heat poorly, then the temperature of the body, if left to itself, will remain practically constant for a long time. Such ideal shells, of course, do not exist in nature, but shells can be created that approach these in their properties.

Examples are cladding spaceships, Dewar vessels used in physics and technology. The Dewar vessel is a glass or metal container with double mirrored walls, between which a high vacuum is created. The glass flask of a home thermos is also a Dewar vessel.

The shell is insulating calorimeter- a device that measures the amount of heat. The calorimeter is a large thin-walled glass, placed on pieces of cork inside another large glass so that a layer of air remains between the walls, and closed from above with a heat-resistant lid.

If in the calorimeter two or more bodies with various temperatures, and wait, then after some time thermal equilibrium will be established inside the calorimeter. In the process of transition to thermal equilibrium, some bodies will give off heat (the total amount of heat `Q_(sf"otd")`), others will receive heat (the total amount of heat `Q_(sf"floor")`). And since the calorimeter and the bodies contained in it do not exchange heat with the surrounding space, but only between themselves, we can write the relation, also called heat balance equation:

In a number of thermal processes, heat can be absorbed or released by a body without changing its temperature. Such thermal processes take place when the aggregate state of a substance changes - melting, crystallization, evaporation, condensation and boiling. Let us briefly dwell on the main characteristics of these processes.

Melting- the process of transformation of a crystalline solid into a liquid. The melting process takes place at constant temperature, heat is absorbed.

The specific heat of fusion `lambda` is equal to the amount of heat required to melt `1` kg of a crystalline substance taken at the melting point. The amount of heat `Q_(sf"pl")`, which is required to transfer a solid body of mass `m` at a melting point into a liquid state, is equal to

Since the melting temperature remains constant, the amount of heat imparted to the body goes to increase the potential energy of molecular interaction, and the crystal lattice is destroyed.

Process crystallization is the reverse process of melting. During crystallization, the liquid turns into a solid body and the amount of heat is released, which is also determined by formula (1.5).

Evaporation is the process of converting liquid into vapor. Evaporation occurs from the open surface of the liquid. In the process of evaporation, the fastest molecules leave the liquid, i.e., molecules that can overcome the forces of attraction from the molecules of the liquid. As a result, if the liquid is thermally insulated, then in the process of evaporation it cools.

The specific heat of vaporization `L` is equal to the amount of heat required to turn `1` kg of liquid into steam. The amount of heat `Q_(sf"isp")`, which is required to convert a liquid of mass `m` into a vapor state is equal to

`Q_(sf"sp") =L*m`.

(1.6)

Condensation is a process that is the reverse of evaporation. When condensed, the vapor turns into a liquid. This releases heat. The amount of heat released during the condensation of steam is determined by formula (1.6).

Boiling is a process in which the pressure saturated vapors liquid equals atmospheric pressure, therefore, evaporation occurs not only from the surface, but also throughout the volume (there are always air bubbles in the liquid, when boiling, the vapor pressure in them reaches atmospheric pressure, and the bubbles rise up).

>>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 quantity numerically equal to the amount of heat that a substance of 1 kg mass receives or gives away 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.
liquid and solid bodies 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 it depend on specific heat 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 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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Learning objective: Introduce the concepts of heat quantity and specific heat capacity.

Developmental goal: To cultivate mindfulness; learn to think, draw conclusions.

1. Topic update

2. Explanation of new material. 50 min.

You already know that the internal energy of a body can change both by doing work and by transferring heat (without doing work).

The energy that a body receives or loses during heat transfer is called the amount of heat. (notebook entry)

This means that the units of measurement of the amount of heat are also Joules ( J).

We conduct an experiment: two glasses in one 300 g of water, and in the other 150 g, and an iron cylinder weighing 150 g. Both glasses are placed on the same tile. After some time, thermometers will show that the water in the vessel in which the body is located heats up faster.

This means that less heat is required to heat 150 g of iron than to heat 150 g of water.

The amount of heat transferred to the body depends on the kind of substance from which the body is made. (notebook entry)

We propose the question: is the same amount of heat required to heat bodies of equal mass, but consisting of different substances, to the same temperature?

We conduct an experiment with the Tyndall device to determine the specific heat capacity.

We conclude: bodies of different substances, but of the same mass, give off when cooled and require a different amount of heat when heated by the same number of degrees.

We draw conclusions:

1. To heat bodies of equal mass, consisting of different substances, to the same temperature, it is required different quantity warmth.

2. Bodies of equal mass, consisting of different substances and heated to the same temperature. When cooled by the same number of degrees, they give off a different amount of heat.

We make the conclusion that the amount of heat required to raise one degree of unit mass of different substances will be different.

We give the definition of specific heat capacity.

The physical quantity, numerically equal to the amount of heat that must be transferred to a body of mass 1 kg in order for its temperature to change by 1 degree, is called the specific heat of the substance.

We introduce the unit of measurement of specific heat capacity: 1J / kg * degree.

The physical meaning of the term : specific heat capacity shows how much the internal energy of 1 g (kg.) of a substance changes when it is heated or cooled by 1 degree.

Consider the table of specific heat capacities of some substances.

We solve the problem analytically

How much heat is required to heat a glass of water (200 g) from 20 0 to 70 0 C.

For heating 1 g per 1 g. Required - 4.2 J.

And to heat 200 g per 1 g, it will take 200 more - 200 * 4.2 J.

And to heat 200 g by (70 0 -20 0) it will take another (70-20) more - 200 * (70-20) * 4.2 J

Substituting the data, we get Q = 200 * 50 * 4.2 J = 42000 J.

We write the resulting formula in terms of the corresponding quantities

4. What determines the amount of heat received by the body when heated?

Please note that the amount of heat required to heat a body is proportional to the mass of the body and the change in its temperature.,

There are two cylinders of the same mass: iron and brass. Is the same amount of heat needed to heat them up by the same number of degrees? Why?

How much heat is needed to heat 250 g of water from 20 o to 60 0 C.

What is the relationship between calories and joules?

A calorie is the amount of heat required to raise the temperature of 1 gram of water by 1 degree.

1 cal = 4.19=4.2 J

1kcal=1000cal

1kcal=4190J=4200J

3. Problem solving. 28 min.

If cylinders of lead, tin and steel heated in boiling water with a mass of 1 kg are placed on ice, they will cool, and part of the ice under them will melt. How will the internal energy of the cylinders change? Under which of the cylinders will melt more ice, under which - less?

A heated stone with a mass of 5 kg. Cooling in water by 1 degree, it transfers 2.1 kJ of energy to it. What is the specific heat capacity of the stone

When hardening a chisel, it was first heated to 650 0, then lowered into oil, where it cooled to 50 0 C. What amount of heat was released if its mass was 500 g.

How much heat was spent on heating from 20 0 to 1220 0 C. a steel billet for the crankshaft of a compressor weighing 35 kg.

Independent work

What type of heat transfer?

Students complete the table.

The air in the room is heated through the walls.
Through open window, which includes warm air.
Through glass, which transmits the rays of the sun.
The earth is heated by the rays of the sun.
The liquid is heated on the stove.
The steel spoon is heated by the tea.
The air is heated by a candle.
The gas moves around the heat-producing parts of the machine.
Heating the barrel of a machine gun.
Boiling milk.

5. Homework: Peryshkin A.V. “Physics 8” §§7, 8; collection of tasks 7-8 Lukashik V.I. Nos. 778-780, 792,793 2 min.

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:

Thus, 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 stock of potential energy, mechanical work by crushing 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. This 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 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 A 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 A 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 state change processes go, which is one of its shortcomings.