Formulas that are suitable for calculating the amount of heat. How to calculate the amount of heat, thermal effect and heat of formation

The concept of the amount of heat was formed on early stages development of modern physics, when there were no clear ideas about internal structure substances, what energy is, what forms of energy exist in nature and energy as a form of movement and transformation of matter.

The amount of heat means physical quantity equivalent to the energy transferred to a material body in the process of heat exchange.

The outdated unit of heat is the calorie, equal to 4.2 J; today this unit is practically not used, and the joule has taken its place.

Initially, it was assumed that the carrier of thermal energy was some completely weightless medium with the properties of a liquid. Numerous physical problems of heat transfer have been and are still being solved based on this premise. The existence of hypothetical caloric was the basis for many essentially correct constructions. It was believed that caloric is released and absorbed in the phenomena of heating and cooling, melting and crystallization. The correct equations for heat transfer processes were obtained based on incorrect physical concepts. There is a known law according to which the amount of heat is directly proportional to the mass of the body participating in heat exchange and the temperature gradient:

Where Q is the amount of heat, m is the body mass, and the coefficient With– a quantity called specific heat capacity. Specific heat capacity is a characteristic of a substance involved in a process.

Work in thermodynamics

As a result of thermal processes, purely mechanical work can be performed. For example, when a gas heats up, it increases its volume. Let's take a situation like the picture below:

IN in this case mechanical work will be equal to the force of gas pressure on the piston multiplied by the path traveled by the piston under pressure. Of course, this is the simplest case. But even in it one can notice one difficulty: the pressure force will depend on the volume of the gas, which means that we are not dealing with constants, but with variable quantities. Since all three variables: pressure, temperature and volume are related to each other, calculating work becomes significantly more complicated. There are some ideal, infinitely slow processes: isobaric, isothermal, adiabatic and isochoric - for which such calculations can be performed relatively simply. A graph of pressure versus volume is plotted and the work is calculated as an integral of the form.

(or heat transfer).

Specific heat capacity of a substance.

Heat capacity- this is the amount of heat absorbed by a body when heated by 1 degree.

The heat capacity of a body is indicated by a capital Latin letter WITH.

What does the heat capacity of a body depend on? First of all, from its mass. It is clear that heating, for example, 1 kilogram of water will require more heat than heating 200 grams.

What about the type of substance? Let's do an experiment. Let's take two identical vessels and pour water weighing 400 into one of them, and into the other - vegetable oil weighing 400 g, let's start heating them using identical burners. By observing the thermometer readings, we will see that the oil heats up quickly. To heat water and oil to the same temperature, the water must be heated longer. But the longer we heat the water, the large quantity it receives heat from the burner.

Thus, to heat the same mass different substances to the same temperature required different quantities warmth. The amount of heat required to heat a body and, therefore, its heat capacity depend on the type of substance of which the body is composed.

So, for example, to increase the temperature of water weighing 1 kg by 1°C, an amount of heat equal to 4200 J is required, and to heat the same mass by 1°C sunflower oil the amount of heat required is 1700 J.

A physical quantity showing how much heat is required to heat 1 kg of a substance by 1 ºС is called specific heat capacity of this substance.

Each substance has its own specific heat capacity, which is denoted by the Latin letter c and measured in joules per kilogram degree (J/(kg °C)).

The specific heat capacity of the same substance in different states of aggregation (solid, liquid and gaseous) is different. For example, the specific heat capacity of water is 4200 J/(kg °C), and the specific heat capacity of ice is 2100 J/(kg °C); aluminum in the solid state has a specific heat capacity of 920 J/(kg - °C), and in the liquid state - 1080 J/(kg - °C).

Note that water has a very high specific heat capacity. Therefore, water in the seas and oceans, heating up in summer, absorbs from the air a large number of heat. Thanks to this, in those places that are located near large bodies of water, summer is not as hot as in places far from the water.

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

From the above it is clear that the amount of heat required to heat a body depends on the type of substance of which the body consists (i.e., its specific heat capacity) and on the mass of the body. It is also clear that the amount of heat depends on how many degrees we are going to increase the body temperature.

So, to determine 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:

Q = cm (t 2 - t 1 ) ,

Where Q- quantity of heat, c— specific heat capacity, m- body mass , t 1 — initial temperature, t 2 — final temperature.

When the body heats up t 2 > t 1 and therefore Q > 0 . When the body cools down t 2i< t 1 and therefore Q< 0 .

If the heat capacity of the entire body is known WITH, Q determined by the formula:

Q = C (t 2 - t 1 ) .

« Physics - 10th grade"

In what processes do aggregate transformations of matter occur?
How can I change state of aggregation substances?

You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
So, when forging a metal, work is done and it heats up, 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 therefore 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, the interaction of slowly moving molecules of a cold body with fast moving molecules of a hot body occurs. As a result, the kinetic energies of the molecules are equalized and the speeds of the molecules of a cold body increase, and those of a hot body decrease.

During heat exchange, energy is not converted from one form to another; part of the internal energy of a more heated body is transferred to a less heated body.

Amount of heat and heat capacity.

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

Q = cm(t 2 - t 1) = cm Δt. (13.5)

When a 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 quantity numerically equal to the amount of heat that a substance weighing 1 kg receives or releases when its temperature changes by 1 K.

The specific heat capacity of gases depends on the process by which heat transfer occurs. If you heat a gas at constant pressure, it will expand and do work. To heat a gas by 1 °C at constant pressure, it needs to transfer more heat than to heat it at a constant volume, when the gas will only heat up.

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

Specific heat of vaporization.

To transform a liquid into steam during the boiling process, a certain amount of heat must be transferred 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 in the potential energy of their interaction. After all, the average distance between gas molecules is much greater than between liquid molecules.

A quantity 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 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. For other liquids, for example 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 vapor, an amount of heat is required equal to:

Q p = rm. (13.6)

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

Q k = -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 between 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 transform a crystalline substance weighing 1 kg at the melting point into a liquid is called specific heat of fusion and denoted by the letter λ.

When a substance weighing 1 kg crystallizes, exactly the same amount of heat is released as is absorbed during melting.

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

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

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

Qpl = λm. (13.8)

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

Q cr = -λm (13.9)

Heat balance equation.

Let us consider heat exchange inside a system consisting of several bodies that initially have different temperatures, for example, heat exchange between water in a vessel and a hot iron ball lowered into the 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 amount of heat given is considered negative, the amount of heat received 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 are the amounts of heat received or given off by 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 during the heat exchange process.

Exercise 81.
Calculate the amount of heat that will be released during the reduction of Fe 2 O 3 metallic aluminum if 335.1 g of iron was obtained. Answer: 2543.1 kJ.
Solution:
Reaction equation:

= (Al 2 O 3) - (Fe 2 O 3) = -1669.8 -(-822.1) = -847.7 kJ

Calculation of the amount of heat that is released when receiving 335.1 g of iron is made from the proportion:

(2 . 55,85) : -847,7 = 335,1 : X; x = (0847.7 . 335,1)/ (2 . 55.85) = 2543.1 kJ,

where 55.85 atomic mass of iron.

Answer: 2543.1 kJ.

Thermal effect of reaction

Task 82.
Gaseous ethanol C2H5OH can be obtained by the interaction of ethylene C 2 H 4 (g) and water vapor. Write the thermochemical equation for this reaction, having first calculated its thermal effect. Answer: -45.76 kJ.
Solution:
The reaction equation is:

C 2 H 4 (g) + H 2 O (g) = C2H 5 OH (g); = ?

The values ​​of standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conventionally assumed to be zero. Let's calculate the thermal effect of the reaction using a consequence of Hess's law, we get:

= (C 2 H 5 OH) – [ (C 2 H 4) + (H 2 O)] =
= -235.1 -[(52.28) + (-241.83)] = - 45.76 kJ

Reaction equations in which about the symbols chemical compounds their states of aggregation or crystalline modification are indicated, as well as the numerical value of thermal effects, called thermochemical. IN thermochemical equations, unless specifically stated, the values ​​of thermal effects at constant pressure Q p are indicated equal to the change in enthalpy of the system. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following abbreviated designations for the state of aggregation of a substance are accepted: G- gaseous, and- liquid, To

If heat is released as a result of a reaction, then< О. Учитывая сказанное, составляем термохимическое уравнение данной в примере реакции:

C 2 H 4 (g) + H 2 O (g) = C 2 H 5 OH (g); = - 45.76 kJ.

Answer:- 45.76 kJ.

Task 83.
Calculate the thermal effect of the reduction reaction of iron (II) oxide with hydrogen based on the following thermochemical equations:

a) EO (k) + CO (g) = Fe (k) + CO 2 (g); = -13.18 kJ;
b) CO (g) + 1/2O 2 (g) = CO 2 (g); = -283.0 kJ;
c) H 2 (g) + 1/2O 2 (g) = H 2 O (g); = -241.83 kJ.
Answer: +27.99 kJ.

Solution:
The reaction equation for the reduction of iron (II) oxide with hydrogen has the form:

EeO (k) + H 2 (g) = Fe (k) + H 2 O (g); = ?

= (H2O) – [ (FeO)

The heat of formation of water is given by the equation

H 2 (g) + 1/2O 2 (g) = H 2 O (g); = -241.83 kJ,

and the heat of formation of iron (II) oxide can be calculated by subtracting equation (a) from equation (b).

=(c) - (b) - (a) = -241.83 – [-283.o – (-13.18)] = +27.99 kJ.

Answer:+27.99 kJ.

Task 84.
When gaseous hydrogen sulfide and carbon dioxide interact, water vapor and carbon disulfide CS 2 (g) are formed. Write the thermochemical equation for this reaction and first calculate its thermal effect. Answer: +65.43 kJ.
Solution:
G- gaseous, and- liquid, To-- crystalline. These symbols are omitted if the aggregative state of the substances is obvious, for example, O 2, H 2, etc.
The reaction equation is:

2H 2 S (g) + CO 2 (g) = 2H 2 O (g) + CS 2 (g); = ?

The values ​​of standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conventionally assumed to be zero. The thermal effect of a reaction can be calculated using a corollary of Hess's law:

= (H 2 O) + (СS 2) – [(H 2 S) + (СO 2)];
= 2(-241.83) + 115.28 – = +65.43 kJ.

2H 2 S (g) + CO 2 (g) = 2H 2 O (g) + CS 2 (g); = +65.43 kJ.

Answer:+65.43 kJ.

Thermochemical reaction equation

Task 85.
Write the thermochemical equation for the reaction between CO (g) and hydrogen, as a result of which CH 4 (g) and H 2 O (g) are formed. How much heat will be released during this reaction if 67.2 liters of methane were obtained in terms of normal conditions? Answer: 618.48 kJ.
Solution:
Reaction equations in which their state of aggregation or crystal modification, as well as the numerical value of thermal effects are indicated next to the symbols of chemical compounds, are called thermochemical. In thermochemical equations, unless specifically stated, the values ​​of thermal effects at constant pressure Q p equal to the change in enthalpy of the system are indicated. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following abbreviated designations for the state of aggregation of a substance are accepted: G- gaseous, and- something, To- crystalline. These symbols are omitted if the aggregative state of the substances is obvious, for example, O 2, H 2, etc.
The reaction equation is:

CO (g) + 3H 2 (g) = CH 4 (g) + H 2 O (g); = ?

The values ​​of standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conventionally assumed to be zero. The thermal effect of a reaction can be calculated using a corollary of Hess's law:

= (H 2 O) + (CH 4) – (CO)];
= (-241.83) + (-74.84) ​​– (-110.52) = -206.16 kJ.

The thermochemical equation will be:

22,4 : -206,16 = 67,2 : X; x = 67.2 (-206.16)/22?4 = -618.48 kJ; Q = 618.48 kJ.

Answer: 618.48 kJ.

Heat of formation

Task 86.
The thermal effect of which reaction is equal to the heat of formation. Calculate the heat of formation of NO based on the following thermochemical equations:
a) 4NH 3 (g) + 5O 2 (g) = 4NO (g) + 6H 2 O (l); = -1168.80 kJ;
b) 4NH 3 (g) + 3O 2 (g) = 2N 2 (g) + 6H 2 O (l); = -1530.28 kJ
Answer: 90.37 kJ.
Solution:
The standard heat of formation is equal to the heat of reaction of the formation of 1 mole of this substance from simple substances at standard conditions(T = 298 K; p = 1.0325.105 Pa). The formation of NO from simple substances can be represented as follows:

1/2N 2 + 1/2O 2 = NO

Given is reaction (a), which produces 4 mol of NO, and given reaction (b), which produces 2 mol of N2. Oxygen is involved in both reactions. Therefore, to determine the standard heat of formation of NO, we compose the following Hess cycle, i.e., we need to subtract equation (a) from equation (b):

Thus, 1/2N 2 + 1/2O 2 = NO; = +90.37 kJ.

Answer: 618.48 kJ.

Task 87.
Crystalline ammonium chloride is formed by the reaction of ammonia and hydrogen chloride gases. Write the thermochemical equation for this reaction, having first calculated its thermal effect. How much heat will be released if 10 liters of ammonia were consumed in the reaction, calculated under normal conditions? Answer: 78.97 kJ.
Solution:
Reaction equations in which their state of aggregation or crystal modification, as well as the numerical value of thermal effects are indicated next to the symbols of chemical compounds, are called thermochemical. In thermochemical equations, unless specifically stated, the values ​​of thermal effects at constant pressure Q p equal to the change in enthalpy of the system are indicated. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following have been accepted: To-- crystalline. These symbols are omitted if the aggregative state of the substances is obvious, for example, O 2, H 2, etc.
The reaction equation is:

NH 3 (g) + HCl (g) = NH 4 Cl (k). ; = ?

The values ​​of standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conventionally assumed to be zero. The thermal effect of a reaction can be calculated using a corollary of Hess's law:

= (NH4Cl) – [(NH 3) + (HCl)];
= -315.39 – [-46.19 + (-92.31) = -176.85 kJ.

The thermochemical equation will be:

The heat released during the reaction of 10 liters of ammonia in this reaction is determined from the proportion:

22,4 : -176,85 = 10 : X; x = 10 (-176.85)/22.4 = -78.97 kJ; Q = 78.97 kJ.

Answer: 78.97 kJ.

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.

Ability to calculate required amount warmth 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).

Given:	SI
Find:

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.

Required quantity	Designation	Units	Basic formula	Formula for quantity
Quantity of heat