How to find the temperature from the formula for the amount of heat. Quantity of heat. Heat units. Specific heat. Calculation of the amount of heat required to heat the body or released by it during cooling

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

committing over system work,
through thermal interaction.

The transfer of heat to a body is not connected 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 the body with a higher temperature do work on some molecules of the body, which has a lower temperature. In this case, thermal interaction is realized due to thermal conduction. The transfer of energy is also possible with the help of radiation. The system of microscopic processes (pertaining 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 called the energy that is received (or given away) by the body in the process of heat exchange with the surrounding bodies (environment). Heat is denoted, usually by 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 communicated to the system (body), or it can be taken from it. It is believed that if heat is imparted to the system, then it is positive.

The formula for calculating heat with a change in temperature

The elementary amount of heat is denoted as . Note that the element of heat that the system receives (gives off) with a small change in its state is not a total 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 reported to the system, and the temperature changes from T to T + dT, is:

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

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

If the body is homogeneous, and the heat capacity is considered independent of temperature, then the amount of heat () that the body receives when its temperature increases by a value can be calculated as:

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

The 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 the phase transition.

So, to transfer an element of matter from the state solid body in the liquid, he should be informed of the amount of heat () equal to:

where is the specific heat of fusion, dm is the body mass element. In this case, 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 vaporization) required to convert liquid to vapor can be found as:

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

Units for measuring the amount of heat

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

An off-system unit of heat that 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 t 1 =10C, the second mass of water t 2 =60C?

Solution. Let's write the equation heat balance as:

where Q=cmt - the amount of heat prepared after mixing water; Q 1 \u003d cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 \u003d cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.

Equation (1.1) implies:

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

So, we get a system of equations:

Solving it, we get:

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 temperature, 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).

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

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

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.

Experience shows that the amount of heat required to heat a body with a mass m temperature T 1 to temperature T 2 is 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 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 C T is numerically equal to the amount of heat required to change the body temperature by 1 K:

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

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

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

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

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

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

where λ - 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 mass 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 high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 154-155.

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 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