Formulas for calculating the amount of heat. Quantity of heat. Specific heat capacity of a substance

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 it cools.

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 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 specific heat capacity table (Table 1), we find ( specific heat copper, since by condition the glass is copper), (the 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

To learn how to calculate the amount of heat that is necessary to heat the body, we first establish on what quantities it depends.

From the previous paragraph, we already know that this amount of heat depends on the kind of substance of which the body consists (i.e., its specific heat capacity):

Q depends on c .

But that's 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 will be in contact with the heater, the more heat it will receive from it. Therefore, the more the temperature of the body changes during heating, the more heat must be transferred to it.

Let the initial temperature of the body be equal to t initial, and the final temperature - t final. Then the change in body temperature will be expressed by the difference

Δt = t end - t start,

and the amount of heat will depend on this value:

Q depends on Δt.

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

Q depends on m.

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, it is required to determine how much heat is needed to heat an iron part with a mass of 5 kg, provided that its initial temperature is 20 °C, and the final temperature should be 620 °C.

From table 8 we find that the specific heat capacity of iron is c = 460 J/(kg*°C). This means that it takes 460 J to heat 1 kg of iron by 1 °C.

To heat 5 kg of iron by 1 ° C, it will take 5 times more quantity heat, i.e. 460 J * 5 \u003d 2300 J.

To heat iron not by 1 °C, but by Δt = 600 °C, it will take another 600 times more heat, i.e. 2300 J * 600 = 1,380,000 J. Exactly the same (modulo) amount of heat will be released and when this iron is cooled from 620 to 20 °C.

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

When the body is heated, tcon > tini and, therefore, Q > 0. When the body is cooled, tcon< t нач и, следовательно, Q < 0.

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 the body or released by it during cooling?

Exercise 81.
Calculate the amount of heat that will be released during the reduction of Fe 2O3 metallic aluminum if 335.1 g of iron was obtained. Answer: 2543.1 kJ.
Solution:
Reaction equation:

\u003d (Al 2 O 3) - (Fe 2 O 3) \u003d -1669.8 - (-822.1) \u003d -847.7 kJ

Calculation of the amount of heat that is released upon receipt of 335.1 g of iron, we produce 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 gland.

Answer: 2543.1 kJ.

Thermal effect of the 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 previously calculated its thermal effect. Answer: -45.76 kJ.
Solution:
The reaction equation is:

C 2 H 4 (g) + H 2 O (g) \u003d C2H 5 OH (g); = ?

The values ​​of the standard heats of formation of substances are given in special tables. Considering that the heats of formation simple substances conditionally accepted zero. Calculate the thermal effect of the reaction, using the consequence of the Hess law, we get:

\u003d (C 2 H 5 OH) - [ (C 2 H 4) + (H 2 O)] \u003d
= -235.1 -[(52.28) + (-241.83)] = - 45.76 kJ

Reaction equations in which about symbols chemical compounds their states of aggregation or crystalline modification are indicated, as well as numerical value thermal effects are called thermochemical. In thermochemical equations, unless it is specifically stated, the values ​​of thermal effects at constant pressure Q p are indicated equal to the change in the enthalpy of the system. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following abbreviations for the aggregate state of matter 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) \u003d 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) EEO (c) + CO (g) \u003d Fe (c) + 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 oxide (II) with hydrogen has the form:

EeO (k) + H 2 (g) \u003d Fe (k) + H 2 O (g); = ?

\u003d (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 oxide (II) can be calculated if equation (a) is subtracted from equation (b).

\u003d (c) - (b) - (a) \u003d -241.83 - [-283.o - (-13.18)] \u003d + 27.99 kJ.

Answer:+27.99 kJ.

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

2H 2 S (g) + CO 2 (g) \u003d 2H 2 O (g) + CS 2 (g); = ?

The values ​​of the standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conditionally taken equal to zero. The thermal effect of the reaction can be calculated using the corollary e from the Hess law:

\u003d (H 2 O) + (CS 2) - [(H 2 S) + (CO 2)];
= 2(-241.83) + 115.28 – = +65.43 kJ.

2H 2 S (g) + CO 2 (g) \u003d 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 crystalline modification, as well as the numerical value of thermal effects, are indicated near the symbols of chemical compounds, are called thermochemical. In thermochemical equations, unless it is specifically stated, the values ​​of thermal effects at constant pressure Q p are indicated equal to the change in the enthalpy of the system. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following abbreviations for the aggregate state of matter are accepted: G- gaseous, and- something to- crystalline. These symbols are omitted if the aggregate state of substances is obvious, for example, O 2, H 2, etc.
The reaction equation is:

CO (g) + 3H 2 (g) \u003d CH 4 (g) + H 2 O (g); = ?

The values ​​of the standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conditionally taken equal to zero. The thermal effect of the reaction can be calculated using the corollary e from the Hess law:

\u003d (H 2 O) + (CH 4) - (CO)];
\u003d (-241.83) + (-74.84) ​​- (-110.52) \u003d -206.16 kJ.

The thermochemical equation will look like:

22,4 : -206,16 = 67,2 : X; x \u003d 67.2 (-206.16) / 22? 4 \u003d -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 from the following thermochemical equations:
a) 4NH 3 (g) + 5O 2 (g) \u003d 4NO (g) + 6H 2 O (g); = -1168.80 kJ;
b) 4NH 3 (g) + 3O 2 (g) \u003d 2N 2 (g) + 6H 2 O (g); = -1530.28 kJ
Answer: 90.37 kJ.
Solution:
The standard heat of formation is equal to the heat of formation of 1 mol of this substance from simple substances under 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 the reaction (a) in which 4 moles of NO are formed and the reaction (b) is given in which 2 moles of N2 are formed. Both reactions involve oxygen. 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 interaction of gaseous ammonia and hydrogen chloride. Write the thermochemical equation for this reaction, having previously calculated its thermal effect. How much heat will be released if 10 liters of ammonia were consumed in the reaction in terms of normal conditions? Answer: 78.97 kJ.
Solution:
Reaction equations in which their state of aggregation or crystalline modification, as well as the numerical value of thermal effects, are indicated near the symbols of chemical compounds, are called thermochemical. In thermochemical equations, unless it is specifically stated, the values ​​of thermal effects at constant pressure Q p are indicated equal to the change in the enthalpy of the system. The value is usually given on the right side of the equation, separated by a comma or semicolon. The following are accepted to- crystalline. These symbols are omitted if the aggregate state of substances is obvious, for example, O 2, H 2, etc.
The reaction equation is:

NH 3 (g) + HCl (g) \u003d NH 4 Cl (k). ; = ?

The values ​​of the standard heats of formation of substances are given in special tables. Considering that the heats of formation of simple substances are conditionally taken equal to zero. The thermal effect of the reaction can be calculated using the corollary e from the Hess law:

\u003d (NH4Cl) - [(NH 3) + (HCl)];
= -315.39 - [-46.19 + (-92.31) = -176.85 kJ.

The thermochemical equation will look like:

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 \u003d 10 (-176.85) / 22.4 \u003d -78.97 kJ; Q = 78.97 kJ.

Answer: 78.97 kJ.

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

To learn how to calculate the amount of heat that is necessary to heat the body, we first establish on what quantities it depends.
From the previous paragraph, we already know that this amount of heat depends on the kind of substance that the body consists of (i.e., its specific heat capacity):
Q depends on c
But that's 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.

Therefore, the more the temperature of the body changes during heating, the more heat must be transferred to it.

Let the initial temperature of the body be equal to tini, and the final temperature - tfin. Then the change in body temperature will be expressed by the difference:

Finally, everyone knows that for heating, for example, 2 kg of water takes more time (and therefore more heat) than it takes to heat 1 kg of water. This means that the amount of heat required to heat up 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, it is required to determine how much heat is needed to heat an iron part with a mass of 5 kg, provided that its initial temperature is 20 °C, and the final temperature should be 620 °C.

From table 8 we find that the specific heat capacity of iron is c = 460 J/(kg°C). This means that it takes 460 J to heat 1 kg of iron by 1 °C.
To heat 5 kg of iron by 1 °C, 5 times the amount of heat is required, i.e. 460 J * 5 = 2300 J.

To heat iron not by 1 °C, but by A t \u003d 600 ° C, it will take another 600 times more heat, i.e. 2300 J X 600 \u003d 1 380 000 J. Exactly the same (in modulus) amount of heat will be released when this iron cools from 620 to 20 ° C.

So, to find the amount of heat necessary to heat the body or released by it during cooling, you need to multiply the specific heat 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 change. 2. By what formula is the amount of heat required to heat the body or released by it during cooling?

S.V. Gromov, N.A. Motherland, Physics Grade 8

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