As is known, a change in mechanical energy occurs in various mechanical processes. W meh. A measure of the change in mechanical energy is the work of the forces applied to the system:

\\ (~ \\ Delta W_ (meh) \u003d A. \\)

During heat transfer, a change in the internal energy of the body occurs. A measure of the change in internal energy during heat transfer is the amount of heat.

Quantity of heat - This is a measure of the change in internal energy that the body receives (or gives) in the process of heat transfer.

Thus, both work and the amount of heat characterize a change in energy, but are not identical with energy. They do not characterize the state of the system itself, but determine the process of energy transfer from one type to another (from one body to another) when the state changes, and significantly depend on the nature of the process.

The main difference between work and the amount of heat is that work characterizes the process of changing the internal energy of the system, accompanied by the conversion of energy from one type to another (from mechanical to internal). The amount of heat characterizes the process of transfer of internal energy from one body to another (from warmer to less warmed), not accompanied by energy conversions.

Experience shows that the amount of heat needed to heat a body with mass m from temperature T 1 to temperature T 2, calculated by the formula

\\ (~ Q \u003d cm (T_2 - T_1) \u003d cm \\ Delta T, \\ qquad (1) \\)

where c - specific heat of the substance;

\\ (~ c \u003d \\ frac (Q) (m (T_2 - T_1)). \\)

The unit of specific heat in SI is the joule per kilogram-Kelvin (J / (kg · K)).

Specific heat c numerically equal to the amount of heat that must be reported to a body weighing 1 kg in order to heat it by 1 K.

Heat capacity body C T is numerically equal to the amount of heat required to change the body temperature by 1 K:

\\ (~ C_T \u003d \\ frac (Q) (T_2 - T_1) \u003d cm. \\)

The unit of heat capacity of the body in SI is the joule on Kelvin (J / K).

To turn liquids into steam at a constant temperature, it is necessary to expend the amount of heat

\\ (~ Q \u003d Lm, \\ qquad (2) \\)

where L - specific heat of vaporization. When steam condenses, the same amount of heat is released.

In order to melt a crystalline solid mass m at the melting temperature, the body needs to report the amount of heat

\\ (~ Q \u003d \\ lambda m, \\ qquad (3) \\)

where λ - specific heat of fusion. When the body crystallizes, the same amount of heat is released.

The amount of heat that is released during the complete combustion of fuel by mass m,

\\ (~ Q \u003d qm, \\ qquad (4) \\)

where q - specific heat of combustion.

The unit specific heat of vaporization, melting and combustion in SI is the joule per kilogram (J / kg).

Literature

Aksenovich L.A. Physics in high school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn .: Adukatsy I vykhavanne, 2004 .-- C. 154-155.

721. Why is water used to cool some mechanisms?
Water has a large specific heat capacity, which contributes to a good heat dissipation from the mechanism.

722. In which case do you need to spend more energy: to heat 1 liter of water by 1 ° C or to heat 100 grams of water by 1 ° C?
To heat a liter of water, since the larger the mass, the more energy is needed.

723. Cupronickel and silver forks of the same mass were lowered into hot water. Will they get the same amount of heat water?
Cupronickel fork will get more heat, because the specific heat of cupronickel is more than silver.

724. A piece of lead and a piece of cast iron of the same mass were hit three times with a sledgehammer. Which piece is hotter?
Lead will heat up more because its specific heat is less than cast iron, and less energy is needed to heat the lead.

725. Water is in one flask, and kerosene of the same mass and temperature is in the other. An equally heated iron cube was thrown into each flask. What will heat up to more high temperature - water or kerosene?
Kerosene.

726. Why are cities on the seashore temperature fluctuations in winter and summer less severe than in cities located inland?
Water heats and cools more slowly than air. In winter, it cools down and moves warm masses of air to land, making the climate on the coast warmer.

727. The specific heat of aluminum is 920 J / kg ° C. What does this mean?
This means that for heating 1 kg of aluminum at 1 ° C, it is necessary to spend 920 J.

728. Aluminum and copper bars of the same mass of 1 kg are cooled at 1 ° C. How much will the internal energy of each bar change? Which bar will it change more and by how much?

729. How much heat is needed to heat a kilogram iron billet at 45 ° C?

730. How much heat is required to heat 0.25 kg of water from 30 ° C to 50 ° C?

731. How will the internal energy of two liters of water change when heated by 5 ° C?

732. How much heat is needed to heat 5 g of water from 20 ° C to 30 ° C?

733. How much heat is needed to heat an aluminum ball weighing 0.03 kg at 72 ° C?

734. Calculate the amount of heat required to heat 15 kg of copper at 80 ° C.

735. Calculate the amount of heat required to heat 5 kg of copper from 10 ° C to 200 ° C.

736. How much heat is required to heat 0.2 kg of water from 15 ° C to 20 ° C?

737. Water weighing 0.3 kg cooled by 20 ° C. How much has the internal energy of water decreased?

738. How much heat is needed to heat 0.4 kg of water at a temperature of 20 ° C to a temperature of 30 ° C?

739. How much heat is used to heat 2.5 kg of water at 20 ° C?

740. How much heat was released when 250 g of water cooled from 90 ° C to 40 ° C?

741. How much heat is needed to heat 0.015 liters of water at 1 ° C?

742. Calculate the amount of heat required to heat a pond with a volume of 300 m3 at 10 ° C?

743. How much heat should be reported to 1 kg of water in order to increase its temperature from 30 ° C to 40 ° C?

744. Water with a volume of 10 l has cooled from a temperature of 100 ° C to a temperature of 40 ° C. How much heat was released?

745. Calculate the amount of heat required to heat 1 m3 of sand at 60 ° C.

746. Air volume 60 m3, specific heat 1000 J / kg ° C, air density 1.29 kg / m3. How much heat is needed to heat it at 22 ° C?

747. Water was heated at 10 ° C, spending 4.20 103 J of heat. Determine the amount of water.

748. Water weighing 0.5 kg reported 20.95 kJ of heat. What was the water temperature if the initial water temperature was 20 ° C?

749. 8 kg of water are poured into a copper pan weighing 2.5 kg at 10 ° C. How much heat is needed to heat the water in a pan to a boil?

750. A liter of water at a temperature of 15 ° C is poured into a copper ladle weighing 300 g. How much heat is needed to heat water in a ladle at 85 ° C?

751. A piece of heated granite weighing 3 kg is placed in water. Granite transfers 12.6 kJ of heat to water, cooling by 10 ° С. What is the specific heat of stone?

752. To 5 kg of water at 12 ° C, hot water was added at 50 ° C, obtaining a mixture at a temperature of 30 ° C. How much water was added?

753. In 3 l of water at 60 ° C, water was added at 20 ° C, receiving water at 40 ° C. How much water was added?

754. What will be the temperature of the mixture if we mix 600 g of water at 80 ° C with 200 g of water at 20 ° C?

755. A liter of water at 90 ° C was poured into water at 10 ° C, and the water temperature became 60 ° C. How much was cold water?

756. Determine how much to pour into a vessel of hot water heated to 60 ° C, if 20 l of cold water is already in the vessel at a temperature of 15 ° C; the temperature of the mixture should be 40 ° C.

757. Determine how much heat is required to heat 425 g of water at 20 ° C.

758. How many degrees will 5 kg of water heat up if the water gets 167.2 kJ?

759. How much heat will it take to heat m grams of water at a temperature t1 to a temperature t2?

760. 2 kg of water is poured into the calorimeter at a temperature of 15 ° C. To what temperature will the water of the calorimeter be heated if a brass weight of 500 g, heated to 100 ° C, is lowered into it? The specific heat capacity of brass is 0.37 kJ / (kg ° C).

761. There are equal volumes of pieces of copper, tin and aluminum. Which of these pieces has the largest and the smallest heat capacity?

762. 450 g of water was poured into the calorimeter, the temperature of which was 20 ° C. When 200 g of iron filings heated to 100 ° C were immersed in this water, the water temperature became 24 ° C. Determine the specific heat of sawdust.

763. A copper calorimeter weighing 100 g contains 738 g of water, the temperature of which is 15 ° C. 200 g of copper was lowered into this calorimeter at a temperature of 100 ° C, after which the temperature of the calorimeter rose to 17 ° C. What is the specific heat of copper?

764. A steel ball weighing 10 g was removed from the furnace and lowered into water with a temperature of 10 ° C. The water temperature rose to 25 ° C. What was the temperature of the ball in the furnace if the mass of water was 50 g? The specific heat capacity of steel is 0.5 kJ / (kg ° C).

770. A steel cutter weighing 2 kg was heated to a temperature of 800 ° C and then lowered into a vessel containing 15 l of water at a temperature of 10 ° C. To what temperature is the water in the vessel heated?

(Note. To solve this problem, it is necessary to draw up an equation in which for the unknown take the desired temperature of the water in the vessel after lowering the cutter.)

771. What temperature will water get if you mix 0.02 kg of water at 15 ° C, 0.03 kg of water at 25 ° C, and 0.01 kg of water at 60 ° C?

772. For heating a well-ventilated class, a heat quantity of 4.19 MJ per hour is required. Water enters the radiators at 80 ° C, and leaves them at 72 ° C. How much water should be supplied to radiators every hour?

773. Lead with a mass of 0.1 kg at a temperature of 100 ° C was immersed in an aluminum calorimeter weighing 0.04 kg containing 0.24 kg of water at a temperature of 15 ° C. After that, a temperature of 16 ° C was established in the calorimeter. What is the specific heat of lead?

In this lesson, we will learn how to calculate the amount of heat needed to heat the body or released by it during cooling. To do this, we summarize the knowledge that was obtained in previous lessons.

In addition, we will learn 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 heating the body or emitted by it during cooling.

Ability to calculate required amount warmth is very important. This may be necessary, for example, when calculating the amount of heat that must be communicated to the water to heat the room.

Fig. 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 burning fuel in various engines:

Fig. 2. The amount of heat that is released during the combustion of fuel in the engine

Also, this knowledge is needed, for example, to determine the amount of heat that is released by the Sun and enters the Earth:

Fig. 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, usually, can be measured using weights);
• the temperature difference by which it is necessary to heat the body or cool it (usually measured using a thermometer);
• specific heat of the body (which can be determined from the table).

Fig. 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 of a substance is measured in;

- temperature difference, measured in degrees Celsius ().

Consider the problem of calculating the amount of heat.

A task

In a copper beaker weighing grams is water volume of a liter at a temperature. How much heat must be transferred to a glass of water so that its temperature becomes equal?

Fig. 5. Illustration of the problem condition

First, write a short condition ( Given) and translate all the quantities into the international system (SI).

Decision:

First, determine what other quantities we need to solve this problem. According to the table of specific heat (table. 1) we find (specific heat of copper, since the glass is copper by condition), (specific heat of water, since by condition the water is in the glass). In addition, we know that to calculate the amount of heat we need a mass of water. By condition, only volume is given to us. Therefore, from the table we take the density of water: (table. 2).

Tab. 1. The specific heat of some substances

Tab. 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 needed to heat the copper cup and the amount of heat needed to heat the water in it:

We first calculate the amount of heat required to heat a copper cup:

Before calculating the amount of heat required to heat the water, we calculate the mass of water according to a formula that is familiar to us from class 7:

Now we can calculate:

Then we can calculate:

Recall what it means: kilojoules. The prefix "kilo" means, that is .

Answer:.

For convenience, solving the 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.

1. The change in internal energy by doing work is characterized by the magnitude of the work, i.e. work is a measure of the change in internal energy in a given process. The change in the internal energy of the body during heat transfer is characterized by a value called amount of heat.

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

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

When a certain amount of heat is transferred to the body without doing work, its internal energy increases, if the body gives up some amount of heat, then its internal energy decreases.

2. If you pour in two identical vessels in one 100 g of water, and in another 400 g at the same temperature and put them on the same burner, then earlier the water will boil in the first vessel. Thus, the greater the mass of the body, the greater the amount of heat it requires for heating. The same thing with cooling: a body of a larger mass gives off more heat when cooled. These bodies are made of the same substance and they are heated or cooled by the same number of degrees.

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

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

5. The dependence of the amount of heat required to heat the body on the type of substance is characterized by a physical quantity called specific heat substance.

A physical quantity equal to the amount of heat that needs to be reported 1 kg of a substance to heat it at 1 ° C (or 1 K) is called the specific heat of the substance.

The same amount of heat gives 1 kg of substance when cooled by 1 ° C.

The specific heat is indicated by the letter \\ (c \\). The unit of specific heat is 1 J / kg ° C or 1 J / kg K.

The specific heat of substances is determined experimentally. Liquids have a higher specific heat capacity than metals; water has the largest specific heat; gold has a very small specific heat.

The specific heat capacity of lead is 140 J / kg ° C. This means that in order to heat 1 kg of lead per 1 ° C, it is necessary to spend 140 J of heat. The same amount of heat will be released when 1 kg of water is cooled at 1 ° C.

Since the amount of heat is equal to the change in the internal energy of the body, we can say that the specific heat shows how much the internal energy of 1 kg of substance changes when its temperature changes by 1 ° C. In particular, the internal energy of 1 kg of lead increases by 140 J when heated by 1 ° C, and decreases by 140 J when cooled.

The amount of heat \\ (Q \\) needed to heat a body of mass \\ (m \\) from temperature \\ ((t_1 \\, ^ \\ circ C) \\) to temperature \\ ((t_2 \\, ^ \\ circ C) \\) is equal to the product of the specific heat of the substance, body weight and the difference between the final and initial temperatures, i.e.

\\ [Q \u003d cm (t_2 () ^ \\ circ-t_1 () ^ \\ circ) \\]

According to the same formula, the amount of heat that the body gives off when it is cooled is also calculated. Only in this case should the final temperature be taken away from the initial temperature, i.e. subtract the lower from the higher temperature.

6. Problem solving example. In a glass containing 200 g of water at a temperature of 80 ° C, 100 g of water was poured at a temperature of 20 ° C. After that, a temperature of 60 ° C was established in the vessel. How much heat did cold water receive and do hot water return?

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

1. write down briefly the condition of the problem;
2. translate the values \u200b\u200bof the values \u200b\u200bin SI;
3. analyze the task, establish which bodies are involved in heat transfer, which bodies give energy and which receive;
4. solve the problem in general view;
5. perform calculations;
6. analyze the response received.

1. The task.

Given:
\\ (M_1 \\) \u003d 200 g
\\ (M_2 \\) \u003d 100 g
\\ (T_1 \\) \u003d 80 ° C
\\ (T_2 \\) \u003d 20 ° C
\\ (T \\) \u003d 60 ° C
______________

\\ (Q_1 \\) -? \\ (Q_2 \\) -?
\\ (C_1 \\) \u003d 4200 J / kg ° C

2. SI: \\ (M_1 \\) \u003d 0.2 kg; \\ (M_2 \\) \u003d 0.1 kg.

3. Task analysis. The task describes the process of heat exchange between hot and cold water. Hot water gives off the amount of heat \\ (Q_1 \\) and cools from temperature \\ (t_1 \\) to temperature \\ (t \\). Cold water receives the amount of heat \\ (Q_2 \\) and heats up from the temperature \\ (t_2 \\) to the temperature \\ (t \\).

4. General solution to the problem. The amount of heat given off by hot water is calculated by the formula: \\ (Q_1 \u003d c_1m_1 (t_1-t) \\).

The amount of heat obtained by cold water is calculated by the formula: \\ (Q_2 \u003d c_2m_2 (t-t_2) \\).

5. Calculations.
\\ (Q_1 \\) \u003d 4200 J / kg · ° С · 0.2 kg · 20 ° С \u003d 16800 J
\\ (Q_2 \\) \u003d 4200 J / kg · ° С · 0.1 kg · 40 ° С \u003d 16800 J

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

Part 1

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

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

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

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

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

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

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

1) \\ (c_1 \u003d c_2 \\)
2) \\ (c_1\u003e c_2 \\)
3) \\ (c_1 4) the answer depends on the value of the mass of bodies

5. The diagram shows the values \u200b\u200bof the amount of heat transferred to two bodies of equal mass when their temperature changes by the same number of degrees. What is the correct ratio for the specific heat capacities of the substances from which the bodies are made?

1) \\ (c_1 \u003d c_2 \\)
2) \\ (c_1 \u003d 3c_2 \\)
3) \\ (c_2 \u003d 3c_1 \\)
4) \\ (c_2 \u003d 2c_1 \\)

6. The figure shows a graph of the temperature of a solid body from the amount of heat given to it. Body weight 4 kg. What is the specific heat capacity of the substance of this body?

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

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

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

8. In order to heat 192 g of molybdenum per 1 K, you need to transfer 48 heat to it. What is the specific heat of this substance?

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

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

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

10. The same amount of heat was expended for heating a brick from 20 to 85 ° С as for heating water of the same mass by 13 ° С. The specific heat of the brick is

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

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

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

12. The table shows the results of measurements of mass \\ (m \\), temperature change \\ (\\ Delta t \\) and the amount of heat \\ (Q \\) released during cooling of cylinders made of copper or aluminum.

What statements correspond to the results of the experiment? From the proposed list, select two correct ones. Indicate their numbers. Based on the measurements, it can be argued that the amount of heat released during cooling,

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

Part 2

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

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

The answers

« Physics - Grade 10 "

In what processes do aggregate transformations of a substance take place?
How can the aggregate state of a substance be changed?

You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
So, when forging metal, work is done, and it is heated, at the same time, the metal can be heated above a burning flame.

Also, if the piston is fixed (Fig. 13.5), then the volume of gas does not change during heating and work is not completed. But the temperature of the gas and, consequently, its internal energy increase.

Internal energy can increase and decrease, so the amount of heat can be positive and negative.

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

A quantitative measure of changes in internal energy during heat transfer is called amount of heat.

Molecular picture of heat transfer.

During heat transfer at the interface between the bodies, the slowly moving molecules of the cold body interact with the fast-moving molecules of the hot body. As a result, the kinetic energies of the molecules are aligned and the velocities of the molecules of the cold body increase, while those of the hot one decrease.

During heat transfer, there is no conversion of energy from one form to another, part of the internal energy of a warmer body is transferred to a less heated body.

The amount of heat and heat capacity.

You already know that for heating a body of mass m from temperature t 1 to temperature t 2 it is necessary to transfer the amount of heat to it:

Q \u003d cm (t 2 - t 1) \u003d cm Δt. (13.5)

When the body cools, its final 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 the formula (13.5) is called specific heat substances.

Specific heat is a quantity numerically equal to the amount of heat that a substance weighing 1 kg receives or gives off when its temperature changes by 1 K.

The specific heat capacity of gases depends on which process the heat transfer is carried out. If you heat the gas at constant pressure, it will expand and do the job. To heat the gas at 1 ° C at constant pressure, it needs to transfer a greater amount of 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 a constant volume and constant pressure do not differ much.

Specific heat of vaporization.

To turn liquid into steam during the boiling process, a certain amount of heat must be transferred to it. The temperature of the liquid during boiling does not change. 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 larger than between liquid molecules.

A value that is 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 is expressed in joules per kilogram (J / kg).

The specific heat of water vaporization is very high: r Н20 \u003d 2.256 10 6 J / kg at a temperature of 100 ° C. Other liquids, such as alcohol, ether, mercury, kerosene, have a specific heat of vaporization of 3-10 times less than that of water.

To convert a liquid of mass m into steam, an amount of heat equal to:

Q p \u003d rm. (13.6)

During steam condensation, the same amount of heat is released:

Q to \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 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 and are denoted by the letter λ.

During crystallization of a substance weighing 1 kg, exactly the same amount of heat is released that is absorbed during melting.

The specific heat of melting ice is quite high: 3.34 10 5 J / kg.

“If the ice did not have a high heat of melting, then in the spring the entire mass of ice would have to melt in a few minutes or seconds, since the heat is continuously transferred to the ice from the air. The consequences of this would be terrible; after all, even in the current situation, large floods and strong water flows arise during the melting of large masses of ice or snow. " R. Black, XVIII century

In order to melt a crystalline body of mass m, an amount of heat equal to:

Q pl \u003d λm. (13.8)

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

Q cr \u003d -λm (13.9)

The equation of heat balance.

Consider heat transfer within a system consisting of several bodies having initially different temperatures, for example heat transfer between water in a vessel and a hot iron ball immersed in water. According to the law of conservation of energy, the amount of heat given by one body is numerically equal to the amount of heat received by another.

A given amount of heat is considered negative, a received amount of heat is considered positive. Therefore, the total amount of heat Q1 + Q2 \u003d 0.

If in an isolated system there is heat exchange between several bodies, then

Q 1 + Q 2 + Q 3 + ... \u003d 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 bodies. These quantities of heat are expressed by the formula (13.5) or formulas (13.6) - (13.9) if various phase transformations of the substance occur during heat exchange (melting, crystallization, vaporization, condensation).