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 a solid state to a liquid, it 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:
Outline plan
open lesson physics in 8 "E" class
MOU gymnasium No. 77, o. Tolyatti
physics teachers
Ivanova Maria Konstantinovna
Lesson topic:
Solving problems for calculating the amount of heat required to heat the body or released by it during cooling.
The date of the:
The purpose of the lesson:
to develop practical skills in calculating the amount of heat required for heating and released during cooling;
develop counting skills, improve logical skills in analyzing the plot of problems, solving qualitative and computational problems;
to cultivate the ability to work in pairs, respect the opinion of the opponent and defend their point of view, be careful when completing tasks in physics.
Lesson equipment:
computer, projector, presentation on the topic (Appendix No. 1), materials single collection digital educational resources.
Lesson type:
problem solving.
“Put your finger into the flame from a match, and you will experience a sensation that is not equal in heaven or on earth; however, everything that has happened is simply the result of collisions of molecules.
J. Wheeler
During the classes:
Organizing time
Greeting students.
Checking for absent students.
Presentation of the topic and objectives of the lesson.
Checking homework.
1.Frontal survey
What is the specific heat capacity of a substance? (Slide #1)
What is the unit of specific heat capacity of a substance?
Why do bodies of water freeze slowly? Why doesn’t ice leave rivers and especially lakes for a long time, although the weather has been warm for a long time?
Why is it warm enough on the Black Sea coast of the Caucasus even in winter?
Why Do Many Metals Cool Down Significantly? faster than water? (Slide #2)
2. Individual survey (cards with multi-level tasks for several students)
Exploring a new topic.
1. Repetition of the concept of the amount of heat.
Quantity of heat- a quantitative measure of the change in internal energy during heat transfer.
The amount of heat absorbed by the body is considered to be positive, and the amount of heat released is negative. The expression “the body has a certain amount of heat” or “the body contains (stored) some amount of heat” does not make sense. The amount of heat can be received or given away in any process, but it cannot be possessed.
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 aligned 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 hot body is transferred to a cold body.
2. The formula for the amount of heat.
We derive a working formula to solve problems for calculating the amount of heat: Q = cm ( t 2 - t 1 ) - writing on the board and in notebooks.
We find out that the amount of heat given or received by the body depends on the initial temperature of the body, its mass and its specific heat capacity.
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.
3 . The dependence of the amount of heat on various quantities . (Slides #3, #4, #5, #6)
4 . Specific heat (Slide number 7)
5. Units for measuring the amount of heat (Slide number 8)
6. An example of solving a problem for calculating the amount of heat (Slide number 10)
7. Solving problems for calculating the amount of heat on the board and in notebooks
We also find out 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. To do this, we use an example of a solved problem from § 9 of the textbook.
Dynamic pause.
IV. Consolidation of the studied material.
1. Questions for self-control (Slide number 9)
2. Solving quality problems:
Why is it hot in deserts during the day, but at night the temperature drops below 0°C? (Sand has a low specific heat capacity, so it heats up and cools down quickly.)
A piece of lead and a piece of steel of the same mass were hit with a hammer the same number of times. Which piece got hotter? Why? (The piece of lead heated up more, because the specific heat capacity of lead is less.)
Why do iron stoves heat up a room faster than brick stoves, but do not stay warm for so long? (Specific heat less copper than brick.)
Copper and steel weights of the same mass are given equal amounts of heat. Which weight will change the temperature the most? (At copper, because the specific heat capacity of copper is less.)
What consumes more energy: heating water or heating an aluminum pan, if their masses are the same? (For heating water, because the specific heat capacity of water is large.)
As you know, iron has a higher specific heat capacity than copper. Consequently, a stinger made of iron would have a greater supply of internal energy than the same sting made of copper, if their masses and temperatures are equal. Why, despite this, are soldering iron tips made of copper? (Copper has great thermal conductivity.)
It is known that the thermal conductivity of metal is much greater than the thermal conductivity of glass. Why, then, are calorimeters made of metal and not glass? (The metal has a high thermal conductivity and low specific heat, due to which the temperature inside the calorimeter quickly equalizes, and little heat is spent on heating it. In addition, metal radiation is much less than glass radiation, which reduces heat loss.)
It is known that loose snow protects the soil well from freezing, because it contains a lot of air, which is a poor conductor of heat. But after all, even layers of air adjoin the soil that is not covered with snow. Why, then, does she not freeze much in this case? (The air, in contact with the soil not covered with snow, is constantly in motion, mixed. This moving air removes heat from the earth and increases the evaporation of moisture from it. The air, which is between the particles of snow, is inactive and, as a poor conductor of heat, protects the earth from freezing.)
3. Solution of calculation problems
The first two tasks are solved by highly motivated students at the blackboard with collective discussion. We find the right approaches in reasoning and solving problems.
Task #1.
When heating a piece of copper from 20°C to 170°C, 140,000 J of heat were expended. Determine the mass of copper.
Task #2
What is the specific heat capacity of a liquid if it took 150,000 J to heat 2 liters of it by 20 ° C. The density of the liquid is 1.5 g / cm³
Students answer the following questions in pairs:
Task number 3.
Two copper balls of mass m o and 4m o heated so that both balls receive the same amount of heat. At the same time, the large ball heated up by 5°C. How much did the ball of smaller mass heat up?
Task number 4.
How much heat is released when 4 m³ of ice is cooled from 10°C to -40°C?
Task number 5.
In which case will more heat be required to heat two substances if the heating of two substances is the same ∆ t 1 = ∆t 2 The first substance is a brick with a mass of 2 kg and s = 880 J / kg ∙ ° C, and brass - a mass of 2 kg and s \u003d 400 J / kg ∙ ° C
Task number 6.
A steel bar of mass 4 kg is heated. In this case, 200,000 J of heat were spent. Determine the final body temperature if the initial temperature is t 0 = 10°C
When students solve problems on their own, it is natural that questions arise. The most frequently asked questions are discussed collectively. Those questions that are of a private nature are given individual answers.
Reflection. Putting marks.
Teacher: So, guys, what did you learn in the lesson today and what did you learn new?
Sample student responses :
Worked out the skills of solving qualitative and computational problems on the topic "Calculation of the amount of heat required to heat the body and released during cooling."
We were convinced in practice how such subjects as physics and mathematics overlap and are connected.
Homework:
Solve problems No. 1024, 1025, from the collection of problems by V.I. Lukashik, E. V. Ivanova.
Independently come up with a problem for calculating the amount of heat required to heat the body or released by it during cooling.
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.
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 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.
« Physics - Grade 10 "
In what processes does aggregate transformation of matter occur?
How can you change state of aggregation substances?
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 aligned 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.
liquid and solid bodies 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.
A value numerically equal to the amount of heat required for the transformation crystalline substance weighing 1 kg at the 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).
