The concept of the amount of heat. Calculation of the amount of heat required to heat a body or released by it during cooling

The internal energy of a thermodynamic system can be changed in two ways:

1. doing work on the system,
2. using thermal interaction.

The transfer of heat to a body is not associated with the performance of macroscopic work on the body. In this case, the change in internal energy is caused by the fact that individual molecules of a body with a higher temperature do work on some molecules of a body that has a lower temperature. In this case, thermal interaction is realized due to thermal conductivity. Energy transfer is also possible using radiation. The system of microscopic processes (relating not to the whole body, but to individual molecules) is called heat transfer. The amount of energy that is transferred from one body to another as a result of heat transfer is determined by the amount of heat that is transferred from one body to another.

Definition

Warmth is the energy that is received (or given up) by a body in the process of heat exchange with surrounding bodies (environment).

The symbol for heat is usually the letter Q.

This is one of the basic quantities in thermodynamics. Heat is included in the mathematical expressions of the first and second laws of thermodynamics. Heat is said to be energy in the form of molecular motion.

Heat can be transferred to the system (body), or it can be taken from it. It is believed that if heat is transferred to the system, then it is positive.

Formula for calculating heat when temperature changes

We denote the elementary amount of heat as . Let us note that the element of heat that the system receives (gives) with a small change in its state is not a complete differential. The reason for this is that heat is a function of the process of changing the state of the system.

The elementary amount of heat that is imparted to the system, and the temperature changes from T to T+dT, is equal to:

where C is the heat capacity of the body. If the body in question is homogeneous, then formula (1) for the amount of heat can be represented as:

where is the specific heat capacity of the body, m is the mass of the body, is the molar heat capacity, is the molar mass of the substance, is the number of moles of the substance.

where t 2, t 1 body temperatures before and after heating. Please note that when finding the difference () in calculations, temperatures can be substituted both in degrees Celsius and in kelvins.

Formula for the amount of heat during phase transitions

The transition from one phase of a substance to another is accompanied by the absorption or release of a certain amount of heat, which is called the heat of phase transition.

So, to transfer an element of matter from a solid state to a liquid, it should be given an amount of heat () equal to:

where is the specific heat of fusion, dm is the element of body mass. It should be taken into account that the body must have a temperature equal to the melting point of the substance in question. During crystallization, heat is released equal to (4).

The amount of heat (heat of evaporation) required to convert liquid into vapor can be found as:

where r is the specific heat of evaporation. When steam condenses, heat is released. The heat of evaporation is equal to the heat of condensation of equal masses of substance.

Units for measuring the amount of heat

The basic unit of measurement for the amount of heat in the SI system is: [Q]=J

An extra-system unit of heat, which is often found in technical calculations. [Q]=cal (calorie). 1 cal=4.1868 J.

Examples of problem solving

Example

Exercise. What volumes of water should be mixed to obtain 200 liters of water at a temperature of t = 40C, if the temperature of one mass of water is t 1 = 10 C, the temperature of the second mass of water is t 2 = 60 C?

Solution. Let us write the heat balance equation in the form:

where Q=cmt is the amount of heat prepared after mixing the water; Q 1 = cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 = cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.

From equation (1.1) it follows:

When combining cold (V 1) and hot (V 2) parts of water into a single volume (V), we can assume that:

So, we get a system of equations:

Having solved it we get:

In practice, thermal calculations are often used. For example, when constructing buildings, it is necessary to take into account how much heat the entire heating system should give to the building. You should also know how much heat will escape into the surrounding space through windows, walls, and doors.

We will show with examples how to carry out simple calculations.

So, you need to find out how much heat the copper part received when heated. Its mass was 2 kg, and the temperature increased from 20 to 280 °C. First, using Table 1, we determine the specific heat capacity of copper with m = 400 J / kg °C). This means that heating a copper part weighing 1 kg by 1 °C will require 400 J. To heat a copper part weighing 2 kg by 1 °C, the amount of heat required is 2 times greater - 800 J. The temperature of the copper part must be increased by more than 1 °C, and at 260 °C, this means that 260 times more heat will be required, i.e. 800 J 260 = 208,000 J.

If we denote the mass as m, the difference between the final (t 2) and initial (t 1) temperatures - t 2 - t 1, we obtain a formula for calculating the amount of heat:

Q = cm(t 2 - t 1).

Example 1. An iron cauldron weighing 5 kg is filled with water weighing 10 kg. How much heat must be transferred to the boiler with water to change its temperature from 10 to 100 °C?

When solving the problem, you need to take into account that both bodies - the boiler and the water - will heat up together. Heat exchange occurs between them. Their temperatures can be considered the same, i.e. the temperature of the boiler and water changes by 100 °C - 10 °C = 90 °C. But the amounts of heat received by the boiler and water will not be the same. After all, their masses and specific heat capacities are different.

Heating water in a pot

Example 2. We mixed water weighing 0.8 kg at a temperature of 25 °C and water at a temperature of 100 °C weighing 0.2 kg. The temperature of the resulting mixture was measured, and it turned out to be 40 °C. Calculate how much heat the hot water gave up when cooling and the cold water received when heated. Compare these amounts of heat.

Let's write down the conditions of the problem and solve it.

We see that the amount of heat given off by hot water and the amount of heat received by cold water are equal. This is not a random result. Experience shows that if heat exchange occurs between bodies, then the internal energy of all heating bodies increases by as much as the internal energy of cooling bodies decreases.

When conducting experiments, it usually turns out that the energy given off by hot water is greater than the energy received by cold water. This is explained by the fact that part of the energy is transferred to the surrounding air, and part of the energy is transferred to the vessel in which the water was mixed. The equality of energy given and received will be more accurate, the less energy loss is allowed in the experiment. If you calculate and take into account these losses, the equality will be exact.

Questions

1. What do you need to know to calculate the amount of heat received by a body when heated?
2. Explain with an example how the amount of heat imparted to a body when it is heated or released when it is cooled is calculated.
3. Write a formula to calculate the amount of heat.
4. What conclusion can be drawn from the experiment of mixing cold and hot water? Why are these energies not equal in practice?

Exercise 8

1. How much heat is required to heat 0.1 kg of water by 1 °C?
2. Calculate the amount of heat required to heat: a) a cast iron iron weighing 1.5 kg to change its temperature by 200 °C; b) an aluminum spoon weighing 50 g from 20 to 90 °C; c) a brick fireplace weighing 2 tons from 10 to 40 °C.
3. How much heat was released when water with a volume of 20 liters cooled, if the temperature changed from 100 to 50 °C?

>>Physics: Calculation of the amount of heat required to heat a body and released by it during cooling

To learn how to calculate the amount of heat that is necessary to heat a body, let us first establish on what quantities it depends.
From the previous paragraph we already know that this amount of heat depends on the type of substance of which the body consists (i.e., its specific heat capacity):
Q depends on c
But that is not all.

If we want to heat the water in the kettle so that it becomes only warm, then we will not heat it for long. And in order for the water to become hot, we will heat it longer. But the longer the kettle is in contact with the heater, the more heat it will receive from it.

Consequently, the more the body temperature changes when heated, the greater the amount of heat that needs to be transferred to it.

Let the initial temperature of the body be tbegin, and the final temperature be tend. Then the change in body temperature will be expressed by the difference:

Finally, everyone knows that for heating For example, 2 kg of water requires more time (and therefore more heat) than to heat 1 kg of water. This means that the amount of heat required to heat a body depends on the mass of that body:

So, to calculate the amount of heat, you need to know the specific heat capacity of the substance from which the body is made, the mass of this body and the difference between its final and initial temperatures.

Let, for example, you need to determine how much heat is needed to heat an iron part weighing 5 kg, provided that its initial temperature is 20 °C, and the final temperature should be equal to 620 °C.

From Table 8 we find that the specific heat capacity of iron is c = 460 J/(kg°C). This means that heating 1 kg of iron by 1 °C requires 460 J.
To heat 5 kg of iron by 1 °C, 5 times more heat will be required, i.e. 460 J * 5 = 2300 J.

To heat iron not by 1 °C, but by A t = 600°C, another 600 times more amount of heat will be required, i.e. 2300 J X 600 = 1,380,000 J. Exactly the same (modulo) amount of heat will be released when this iron cools from 620 to 20 °C.

So, to find the amount of heat required to heat a body or released by it during cooling, you need to multiply the specific heat capacity of the body by its mass and by the difference between its final and initial temperatures:

??? 1. Give examples showing that the amount of heat received by a body when heated depends on its mass and temperature changes. 2. What formula is used to calculate the amount of heat required to heat a body or released by it when cooling?

S.V. Gromov, N.A. Rodina, Physics 8th grade

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

In addition, we will learn, using the formula for the amount of heat, to express the remaining quantities from this formula and calculate them, knowing other quantities. An example of a problem with a solution for calculating the amount of heat will also be considered.

This lesson is devoted to calculating the amount of heat when a body is heated or released when cooled.

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

Rice. 1. The amount of heat that must be imparted to the water to heat the room

Or to calculate the amount of heat that is released when fuel is burned in various engines:

Rice. 2. The amount of heat that is released when fuel is burned in the engine

This knowledge is also needed, for example, to determine the amount of heat that is released by the Sun and falls on the Earth:

Rice. 3. The amount of heat released by the Sun and falling on the Earth

To calculate the amount of heat, you need to know three things (Fig. 4):

• body weight (which can usually be measured using a scale);
• the temperature difference by which a body must be heated or cooled (usually measured using a thermometer);
• specific heat capacity of the body (which can be determined from the table).

Rice. 4. What you need to know to determine

The formula by which the amount of heat is calculated looks like this:

The following quantities appear in this formula:

The amount of heat measured in joules (J);

The specific heat capacity of a substance is measured in ;

- temperature difference, measured in degrees Celsius ().

Let's consider the problem of calculating the amount of heat.

Task

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

Rice. 5. Illustration of the problem conditions

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

Solution:

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

Table 1. Specific heat capacity of some substances,

Table 2. Densities of some liquids

Now we have everything we need to solve this problem.

Note that the final amount of heat will consist of the sum of the amount of heat required to heat the copper glass and the amount of heat required to heat the water in it:

Let's first calculate the amount of heat required to heat a copper glass:

Before calculating the amount of heat required to heat water, let’s calculate the mass of water using a formula that is familiar to us from grade 7:

Now we can calculate:

Then we can calculate:

Let's remember what kilojoules mean. The prefix "kilo" means .

Answer:.

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

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

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

During heat exchange, 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 is a measure of the change in internal energy that a body receives (or gives up) during the process of heat exchange.

Thus, both work and the amount of heat characterize the change in energy, but are not identical to energy. They do not characterize the state of the system itself, but determine the process of energy transition 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 a system, accompanied by the transformation 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 more heated to less heated), not accompanied by energy transformations.

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

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

Where c- specific heat capacity of the substance;

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

The SI unit of specific heat capacity is joule per kilogram Kelvin (J/(kg K)).

Specific heat c is numerically equal to the amount of heat that must be imparted 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 body temperature by 1 K:

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

The SI unit of heat capacity of a body is joule per Kelvin (J/K).

To transform a liquid into steam at a constant temperature, it is necessary to expend an amount of heat

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

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

In order to melt a crystalline body weighing m at the melting point, the body needs to communicate the amount of heat

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

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

The amount of heat released during complete combustion of a mass of fuel m,

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

Where q- specific heat of combustion.

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

Literature

Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyhavanne, 2004. - P. 154-155.