The amount of heat when heated. Calculation of the amount of heat during heat transfer, specific heat capacity of a substance. Heat balance equation

The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer. Heat transfer occurs between bodies that have different temperature. When contact is established between bodies with different temperatures, a part of the internal energy is transferred from the body with more high temperature to a body with a lower temperature. The energy transferred to the body as a result of heat transfer is called amount of heat.

Specific heat capacity of a substance:

If the heat transfer process is not accompanied by work, then, based on the first law of thermodynamics, the amount of heat is equal to the change in the internal energy of the body: .

The average energy of the random translational motion of molecules is proportional to the absolute temperature. The change in the internal energy of a body is equal to the algebraic sum of the changes in the energy of all atoms or molecules, the number of which is proportional to the mass of the body, so the change in internal energy and, consequently, the amount of heat is proportional to the mass and temperature change:

The proportionality factor in this equation is called specific heat capacity of a substance. The specific heat capacity indicates how much heat is needed to raise the temperature of 1 kg of a substance by 1 K.

Work in thermodynamics:

In mechanics, work is defined as the product of the modules of force and displacement and the cosine of the angle between them. Work is done when a force acts on a moving body and is equal to the change in its kinetic energy.

In thermodynamics, the motion of a body as a whole is not considered; we are talking about the movement of parts of a macroscopic body relative to each other. As a result, the volume of the body changes, and its velocity remains equal to zero. Work in thermodynamics is defined in the same way as in mechanics, but it is equal to the change not in the kinetic energy of the body, but in its internal energy.

When work is done (compression or expansion), the internal energy of the gas changes. The reason for this is as follows: during elastic collisions of gas molecules with a moving piston, their kinetic energy changes.

Let us calculate the work of the gas during expansion. The gas acts on the piston with a force
, where is the pressure of the gas, and - surface area piston. As the gas expands, the piston moves in the direction of the force for a short distance
. If the distance is small, then the gas pressure can be considered constant. The work of the gas is:

Where
- change in gas volume.

In the process of expanding the gas, it does positive work, since the direction of force and displacement coincide. In the process of expansion, the gas gives off energy to the surrounding bodies.

The work done by external bodies on a gas differs from the work of a gas only in sign
, because the strength acting on the gas is opposite to the force , with which the gas acts on the piston, and is equal to it in absolute value (Newton's third law); and the movement remains the same. Therefore work external forces is equal to:

.

First law of thermodynamics:

The first law of thermodynamics is the law of conservation of energy, extended to thermal phenomena. Law of energy conservation: energy in nature does not arise from nothing and does not disappear: the amount of energy is unchanged, it only changes from one form to another.

In thermodynamics, bodies are considered, the position of the center of gravity of which practically does not change. The mechanical energy of such bodies remains constant, and only the internal energy can change.

Internal energy can be changed in two ways: heat transfer and work. In the general case, the internal energy changes both due to heat transfer and due to the performance of work. The first law of thermodynamics is formulated precisely for such general cases:

The change in the internal energy of the system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:

If the system is isolated, then no work is done on it and it does not exchange heat with the surrounding bodies. According to the first law of thermodynamics the internal energy of an isolated system remains unchanged.

Given that
, the first law of thermodynamics can be written as follows:

The amount of heat transferred to the system goes to change its internal energy and to perform work on external bodies by the system.

Second law of thermodynamics: it is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or in the surrounding bodies.

« Physics - Grade 10 "

In what processes does aggregate transformation of matter occur?
How can the state of matter be changed?

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

Also, if the piston is fixed (Fig. 13.5), then the volume of gas does not change when heated and no work is done. But the temperature of the gas, and hence its internal energy, increases.

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

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

The quantitative measure of the change in internal energy during heat transfer is called amount of heat.

Molecular picture of heat transfer.

During heat exchange at the boundary between bodies, slowly moving molecules of a cold body interact with rapidly moving molecules of a hot body. As a result, the kinetic energies of the molecules are equalized and the velocities of the molecules of a cold body increase, while those of a hot body decrease.

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

The amount of heat and heat capacity.

You already know that in order to heat a body with mass m from temperature t 1 to temperature t 2, it is necessary to transfer to it the amount of heat:

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

When the body cools, its final temperature t 2 turns out to be less than the initial temperature t 1 and the amount of heat given off by the body is negative.

The coefficient c in formula (13.5) is called specific heat capacity substances.

Specific heat- this is a value numerically equal to the amount of heat that a substance with a mass of 1 kg receives or gives off when its temperature changes by 1 K.

The specific heat capacity of gases depends on the process by which heat is transferred. If you heat a gas at constant pressure, it will expand and do work. To heat a gas by 1 °C at constant pressure, it needs to be transferred large quantity heat than for heating 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 the molecules, but is accompanied by an increase potential energy their interactions. 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 vaporization.

The process of liquid evaporation occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of vaporization is equal to the specific heat of vaporization.

This value is denoted by the letter r and is expressed in joules per kilogram (J / kg).

The specific heat of vaporization of water is very high: r H20 = 2.256 10 6 J/kg at a temperature of 100 °C. In other liquids, such as alcohol, ether, mercury, kerosene, the specific heat of vaporization is 3-10 times less than that of water.

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

Q p \u003d rm. (13.6)

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

Q k \u003d -rm. (13.7)

Specific heat of fusion.

When a crystalline body melts, all the heat supplied to it goes to increase the potential energy of interaction of molecules. Kinetic energy molecules does not change, since melting occurs at a constant temperature.

The value numerically equal to the amount of heat required to transform a crystalline substance weighing 1 kg at a melting point into a liquid is called specific heat of fusion and are denoted by the letter λ.

During the crystallization of a substance with a mass of 1 kg, exactly the same amount of heat is released as is absorbed during melting.

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

“If ice did not have a high heat of fusion, then in spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to ice from the air. The consequences of this would be dire; for even under the present situation great floods and great torrents of water arise from the melting of great masses of ice or snow.” R. Black, 18th century

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

Qpl \u003d λm. (13.8)

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

Q cr = -λm (13.9)

Heat balance equation.

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

The given amount of heat is considered negative, the received amount of heat is considered positive. Therefore, the total amount of heat Q1 + Q2 = 0.

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

Q 1 + Q 2 + Q 3 + ... = 0. (13.10)

Equation (13.10) is called heat balance equation.

Here Q 1 Q 2 , Q 3 - the amount of heat received or given away by the bodies. These 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 in the process of heat transfer.

1. The change in internal energy by doing work is characterized by the amount of 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 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 body transfers a certain amount of heat without doing work, its internal energy increases, if a body gives off a certain amount of heat, then its internal energy decreases.

2. If you pour 100 g of water into two identical vessels, and 400 g into another at the same temperature and put them on the same burners, then the water in the first vessel will boil earlier. Thus, the greater the mass of the body, the greater the amount of heat it needs to heat up. The same is with cooling: a body of greater mass, when cooled, gives off a greater amount of heat. These bodies are made of the same substance and they heat up or cool down by the same number of degrees.

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

4. If now 100 g of water is poured into one vessel, and a little water is poured into another similar vessel and a metal body is placed in it so that its mass and the mass of water are 100 g, and the vessels are heated on identical tiles, then it can be seen that in a vessel containing only water will have a lower temperature than one containing water and a metal body. Therefore, in order for the temperature of the contents in both vessels to be the same, a greater amount of heat must be transferred to the water than to the water and the metal body. Thus, the amount of heat required to heat a 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 capacity of a substance.

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

The same amount of heat is given off by 1 kg of a substance when cooled by 1 °C.

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

The values ​​of the specific heat capacity of substances are determined experimentally. Liquids have a higher specific heat capacity than metals; Water has the highest specific heat capacity, gold has a very small specific heat capacity.

The specific heat capacity of lead is 140 J/kg °C. This means that to heat 1 kg of lead by 1 °C, it is necessary to spend an amount of heat of 140 J. The same amount of heat will be released when 1 kg of water cools by 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 capacity shows how much the internal energy of 1 kg of a substance changes when its temperature changes by 1 ° C. In particular, the internal energy of 1 kg of lead, when it is heated by 1 °C, increases by 140 J, and when it is cooled, it decreases by 140 J.

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

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

The same formula is used to calculate the amount of heat that the body gives off when cooled. Only in this case should the final temperature be subtracted from the initial temperature, i.e. from greater value subtract less temperature.

6. Problem solution example. A beaker containing 200 g of water at a temperature of 80°C is poured with 100 g of water at a temperature of 20°C. After that, the temperature of 60 °C was established in the vessel. How much heat is received by the cold water and given off by the hot water?

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

1. write down briefly the condition of the problem;
2. convert values ​​of quantities to SI;
3. analyze the problem, establish which bodies participate in heat exchange, which bodies give off energy, and which ones receive it;
4. solve the problem in general view;
5. perform calculations;
6. analyze the received response.

1. The task.

Given:
\\ (m_1 \) \u003d 200 g
\(m_2 \) \u003d 100 g
​ \ (t_1 \) \u003d 80 ° С
​ \ (t_2 \) \u003d 20 ° С
​ \ (t \) \u003d 60 ° С
______________

​\(Q_1 \) ​ — ? ​\(Q_2 \) ​ — ?
​ \ (c_1 \) ​ \u003d 4200 J / kg ° С

2. SI:\\ (m_1 \) \u003d 0.2 kg; ​ \ (m_2 \) \u003d 0.1 kg.

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

4. Solution of the problem in general form. The amount of heat released hot water, is calculated by the formula: ​\(Q_1=c_1m_1(t_1-t) \) .

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

5. Computing.
​ \ (Q_1 \) \u003d 4200 J / kg ° C 0.2 kg 20 ° C \u003d 16800 J
\ (Q_2 \) \u003d 4200 J / kg ° C 0.1 kg 40 ° C \u003d 16800 J

6. In the answer, it was obtained that the amount of heat given off 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 the water was located 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, an amount of heat of 1 J is released
2) when cooling 250 kg of silver per 1 °C, an amount of heat of 1 J is released
3) when 250 kg of silver cools down by 1 °C, the amount of heat 1 J is absorbed
4) when 1 kg of silver cools by 1 °C, an amount of heat of 250 J is released

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

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

3. When transferring solid body mass ​\(m \) ​\(Q \) ​the body temperature 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 values ​​of the specific heat capacity (​\(c_1 \) ​ and ​\(c_2 \) ) of the substances from which these bodies are made.

1) ​\(c_1=c_2 \) ​
2) ​\(c_1>c_2 \) ​
3) \(c_1 4) the answer depends on the value of the mass of the bodies

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

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

6. The figure shows a graph of the dependence of the temperature of a solid body on the amount of heat given off by 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 a crystalline substance weighing 100 g was heated, the temperature of the substance and the amount of heat imparted to the substance were measured. The measurement data were presented in the form of a table. Assuming that energy losses can be neglected, determine the specific heat capacity 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. To heat 192 g of molybdenum by 1 K, it is necessary to transfer to it an amount of heat of 48 J. What is the specific heat capacity of this substance?

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

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 spent on heating a brick from 20 to 85 °C as for heating water of the same mass by 13 °C. The specific heat capacity of a brick is

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

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

1) The amount of heat that a 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 drops by the same number of degrees.
2) When a substance is cooled, its internal energy increases.
3) The amount of heat that a substance receives when heated goes mainly 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 a body can be changed only by giving it a certain amount of heat

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

What statements are consistent with the results of the experiment? Choose the correct two from the list provided. List their numbers. Based on the measurements carried out, it can be argued that the amount of heat released during cooling,

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

Part 2

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

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

Answers

HEAT EXCHANGE.

1.Heat transfer.

Heat exchange or heat transfer is the process of transferring the internal energy of one body to another without doing work.

There are three types of heat transfer.

1) Thermal conductivity is the heat exchange between bodies in direct contact.

2) Convection is heat transfer in which heat is transferred by gas or liquid flows.

3) Radiation is heat transfer by means of electromagnetic radiation.

2. The amount of heat.

The amount of heat is a measure of the change in the internal energy of a body during heat exchange. Denoted by letter Q.

The unit of measurement of the amount of heat = 1 J.

The amount of heat received by a body from another body as a result of heat transfer can be spent on increasing the temperature (increasing the kinetic energy of molecules) or on changing the state of aggregation (increasing potential energy).

3. Specific heat capacity of a substance.

Experience shows that the amount of heat required to heat a body of mass m from temperature T 1 to temperature T 2 is proportional to the body mass m and the temperature difference (T 2 - T 1), i.e.

Q = cm(T 2 - T 1 ) = withmΔ T,

With is called the specific heat capacity of the substance of the heated body.

The specific heat capacity of a substance is equal to the amount of heat that must be imparted to 1 kg of the substance in order to heat it by 1 K.

Unit of specific heat capacity =.

The heat capacity values ​​of various substances can be found in physical tables.

Exactly the same amount of heat Q will be released when the body is cooled by ΔT.

4. Specific heat of vaporization.

Experience shows that the amount of heat required to convert a liquid into vapor is proportional to the mass of the liquid, i.e.

Q = lm,

where is the coefficient of proportionality L is called the specific heat of vaporization.

The specific heat of vaporization is equal to the amount of heat that is necessary to convert 1 kg of liquid at the boiling point into steam.

Unit of measure for the specific heat of vaporization.

In the reverse process, the condensation of steam, heat is released in the same amount that was spent on vaporization.

5. Specific heat of fusion.

Experience shows that the amount of heat required to transform a solid into a liquid is proportional to the mass of the body, i.e.

Q = λ m,

where the coefficient of proportionality λ is called the specific heat of fusion.

The specific heat of fusion is equal to the amount of heat that is necessary to turn a solid body weighing 1 kg into a liquid at the melting point.

Unit of measure for specific heat of fusion.

In the reverse process, the crystallization of a liquid, heat is released in the same amount that was spent on melting.

6. Specific heat of combustion.

Experience shows that the amount of heat released during the complete combustion of the fuel is proportional to the mass of the fuel, i.e.

Q = qm,

Where the proportionality factor q is called the specific heat of combustion.

The specific heat of combustion is equal to the amount of heat that is released during the complete combustion of 1 kg of fuel.

Unit of measure for specific heat of combustion.

7. Heat balance equation.

Two or more bodies are involved in heat exchange. Some bodies give off heat, while others receive it. Heat transfer occurs until the temperatures of the bodies become equal. According to the law of conservation of energy, the amount of heat that is given off is equal to the amount that is received. On this basis, the heat balance equation is written.

Consider an example.

A body of mass m 1 , whose heat capacity is c 1 , has temperature T 1 , and a body of mass m 2 , whose heat capacity is c 2 , has temperature T 2 . Moreover, T 1 is greater than T 2. These bodies are brought into contact. Experience shows that a cold body (m 2) begins to heat up, and a hot body (m 1) begins to cool. This suggests that part of the internal energy of a hot body is transferred to a cold one, and the temperatures even out. Let us denote the final total temperature by θ.

The amount of heat transferred from a hot body to a cold one

Q transferred. = c 1 m 1 (T 1 – θ )

The amount of heat received by a cold body from a hot one

Q received. = c 2 m 2 (θ – T 2 )

According to the law of conservation of energy Q transferred. = Q received., i.e.

c 1 m 1 (T 1 – θ )= c 2 m 2 (θ – T 2 )

Let us open the brackets and express the value of the total steady-state temperature θ.

The temperature value θ in this case will be obtained in kelvins.

However, since in the expressions for Q passed. and Q is received. if there is a difference between two temperatures, and it is the same in both kelvins and degrees Celsius, then the calculation can be carried out in degrees Celsius. Then

In this case, the temperature value θ will be obtained in degrees Celsius.

The equalization of temperatures as a result of heat conduction can be explained on the basis of molecular kinetic theory as an exchange of kinetic energy between molecules during collision in the process of thermal chaotic motion.

This example can be illustrated with a graph.

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).

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.