Calculation of the approximate required amount of heat. The formula for the amount of heat

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 go into the surrounding space through windows, walls, doors.

We will show by examples how to carry out the simplest calculations.

So, you need to find out how much heat the copper part received when heated. Its mass is 2 kg, and the temperature increased from 20 to 280 °C. First, according to Table 1, we determine the specific heat capacity of copper with m = 400 J / kg ° C). This means that it takes 400 J to heat a copper part weighing 1 kg by 1 °C. To heat a copper part weighing 2 kg by 1 °C, you need 2 times more heat - 800 J. The temperature of the copper part must be increased by more than 1 ° C, and by 260 ° C, it means that 260 times more heat will be required, i.e. 800 J 260 \u003d 208,000 J.

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

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

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

When solving the problem, it must be taken into account that both bodies - both the boiler and the water - will be heated together. Heat exchange takes place 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 kettle

Example 2. Mixed water weighing 0.8 kg, having 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 found to be 40°C. Calculate how much heat the hot water gave off when it cooled and the cold water received when it was heated. Compare these amounts of heat.

Let's write down the condition 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 to each other. 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 water was mixed. The equality of the given and received energies will be the more accurate, the less energy loss is allowed in the experiment. If you calculate and take into account these losses, then the equality will be accurate.

Questions

1. What you need to know to calculate the amount of heat received by the 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 experience of mixing cold and hot water? Why are these energies not equal in practice?

Exercise 8

1. How much heat is required to raise the temperature of 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. What is the amount of heat released during the cooling of water, the volume of which is 20 liters, if the temperature changes from 100 to 50 °C?

As you know, during various mechanical processes, a change in mechanical energy occurs. The measure of change in mechanical energy is the work of forces applied to the system:

During heat transfer, a change in the internal energy of the body occurs. The measure of 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 the body receives (or gives away) in the process of heat transfer.

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 transfer from one form to another (from one body to another) when the state changes and essentially 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 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 of mass m from temperature to temperature is calculated by the formula

where c is the specific heat capacity of the substance;

The SI unit of specific heat is the 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 of mass 1 kg in order to heat it by 1 K.

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

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

To change a liquid into a vapor at a constant temperature, the amount of heat required is

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

In order to melt a crystalline body of mass m at the melting point, it is necessary to inform the body of the amount of heat

where is the specific heat of fusion. During the crystallization of a body, the same amount of heat is released.

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

where q is the specific heat of combustion.

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

« 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 transfer more heat than to heat it at a constant volume, when the gas will only heat up.

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

Specific heat of vaporization.

To convert a liquid into vapor during the boiling process, it is necessary to transfer a certain amount of heat to it. The temperature of a liquid does not change when it boils. The transformation of 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.

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. The kinetic energy of the 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 exchange within a system consisting of several bodies initially having different 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 quantities of heat are expressed by formula (13.5) or formulas (13.6) - (13.9), if various phase transformations of the substance occur in the process of heat transfer (melting, crystallization, vaporization, condensation).

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.

Task

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

Rice. 5. Illustration of the condition of the problem

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

Given:	SI
Find:

Solution:

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

Tab. 1. Specific heat capacity of some substances,

Tab. 2. Densities of some liquids

Now we have everything we need to solve this problem.

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

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

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

Now we can calculate:

Then we can calculate:

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

Answer:.

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

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