Quantity of heat. Lesson topic: "Amount of heat. Units of amount of heat. Specific heat capacity. Calculation of amount of heat"

The internal energy of a body can change due to the work of external forces. To characterize the change in internal energy during heat transfer, a quantity called the amount of heat and denoted Q is introduced.

IN international system The unit of heat, as well as work and energy, is the joule: = = = 1 J.

In practice, a non-systemic unit of heat quantity is sometimes used - the calorie. 1 cal. = 4.2 J.

It should be noted that the term “quantity of heat” is unfortunate. It was introduced at a time when it was believed that bodies contained some weightless, elusive liquid - caloric. The process of heat exchange supposedly consists in the fact that caloric, flowing from one body to another, carries with it a certain amount of heat. Now, knowing the basics of the molecular-kinetic theory of the structure of matter, we understand that there is no caloric in bodies, the mechanism for changing the internal energy of a body is different. However, the power of tradition is great and we continue to use a term introduced on the basis of incorrect ideas about the nature of heat. At the same time, understanding the nature of heat transfer, one should not completely ignore misconceptions about it. On the contrary, by drawing an analogy between the flow of heat and the flow of a hypothetical liquid of caloric, the amount of heat and the amount of caloric, when solving certain classes of problems, it is possible to visualize the ongoing processes and correctly solve the problems. In the end, the correct equations describing heat transfer processes were once obtained on the basis of incorrect ideas about caloric as a heat carrier.

Let us consider in more detail the processes that can occur as a result of heat exchange.

Pour some water into the test tube and close it with a stopper. We hang the test tube from a rod fixed in a stand and place an open flame under it. The test tube receives a certain amount of heat from the flame and the temperature of the liquid in it rises. As the temperature increases, the internal energy of the liquid increases. An intensive process of vaporization occurs. Expanding liquid vapors make mechanical work by pushing a stopper out of a test tube.

Let's conduct another experiment with a model of a cannon made from a piece of brass tube, which is mounted on a cart. On one side the tube is tightly closed with an ebonite plug through which a pin is passed. Wires are soldered to the pin and tube, ending in terminals to which voltage can be supplied from the lighting network. The cannon model is thus a type of electric boiler.

Pour some water into the cannon barrel and close the tube with a rubber stopper. Let's connect the gun to a power source. Electricity, passing through water, heats it. The water boils, which leads to intense steam formation. The pressure of water vapor increases and, finally, they do the work of pushing the plug out of the gun barrel.

The gun, due to recoil, rolls away in the direction opposite to the ejection of the plug.

Both experiences are united by the following circumstances. During the heating process of the liquid different ways, the temperature of the liquid and, accordingly, its internal energy increased. In order for the liquid to boil and evaporate intensively, it was necessary to continue heating it.

Liquid vapors, due to their internal energy, performed mechanical work.

We investigate the dependence of the amount of heat required to heat a body on its mass, temperature changes and the type of substance. To study these dependencies we will use water and oil. (To measure temperature in the experiment, an electric thermometer made of a thermocouple connected to a mirror galvanometer is used. One junction of the thermocouple is lowered into a vessel with cold water to ensure its temperature remains constant. The other junction of the thermocouple measures the temperature of the liquid being tested).

The experience consists of three series. In the first series, for a constant mass of a specific liquid (in our case, water), the dependence of the amount of heat required to heat it on temperature changes is studied. We will judge the amount of heat received by the liquid from the heater (electric stove) by the heating time, assuming that there is a direct relationship between them proportional dependence. For the result of the experiment to correspond to this assumption, it is necessary to ensure a stationary heat flow from the electric stove to the heated body. To do this, the electric stove was turned on in advance, so that by the beginning of the experiment, the temperature of its surface would cease to change. To heat the liquid more evenly during the experiment, we will stir it using the thermocouple itself. We will record the thermometer readings at regular intervals until the light spot reaches the edge of the scale.

Let us conclude: there is a direct proportional relationship between the amount of heat required to heat a body and the change in its temperature.

In the second series of experiments we will compare the amounts of heat required to heat identical liquids of different masses when their temperature changes by the same amount.

For the convenience of comparing the obtained values, the mass of water for the second experiment will be taken to be two times less than in the first experiment.

We will again record the thermometer readings at regular intervals.

Comparing the results of the first and second experiments, the following conclusions can be drawn.

In the third series of experiments we will compare the amounts of heat required to heat equal masses of different liquids when their temperature changes by the same amount.

We will heat oil on an electric stove, the mass of which is equal to the mass of water in the first experiment. We will record the thermometer readings at regular intervals.

The result of the experiment confirms the conclusion that the amount of heat required to heat a body is directly proportional to the change in its temperature and, in addition, indicates the dependence of this amount of heat on the type of substance.

Since the experiment used oil, the density of which is less than the density of water, and heating the oil to a certain temperature required less heat than heating water, it can be assumed that the amount of heat required to heat a body depends on its density.

To test this assumption, we will simultaneously heat equal masses of water, paraffin and copper on a constant power heater.

After the same time, the temperature of copper is approximately 10 times, and paraffin approximately 2 times higher than the temperature of water.

But copper has a higher density and paraffin has a lower density than water.

Experience shows that the quantity characterizing the rate of change in temperature of the substances from which the bodies involved in heat exchange are made is not density. This quantity is called the specific heat capacity of a substance and is denoted by the letter c.

A special device is used to compare the specific heat capacities of different substances. The device consists of racks in which a thin paraffin plate and a strip with rods passed through it are attached. Aluminum, steel and brass cylinders of equal mass are fixed at the ends of the rods.

Let's heat the cylinders to the same temperature by immersing them in a vessel with water standing on a hot stove. We secure the hot cylinders to the racks and release them from the fastening. The cylinders simultaneously touch the paraffin plate and, melting the paraffin, begin to sink into it. The depth of immersion of cylinders of the same mass into a paraffin plate, when their temperature changes by the same amount, turns out to be different.

Experience shows that the specific heat capacities of aluminum, steel and brass are different.

Having carried out appropriate experiments with melting solids, vaporization of liquids, combustion of fuel we obtain the following quantitative dependencies.

To obtain units of specific quantities, they must be expressed from the corresponding formulas and into the resulting expressions substitute units of heat - 1 J, mass - 1 kg, and for specific heat capacity - 1 K.

We get the following units: specific heat capacity – 1 J/kg·K, other specific heats: 1 J/kg.

The internal energy of a body changes when work is performed or heat is transferred. In the phenomenon of heat transfer, internal energy is transferred by conduction, convection or radiation.

Each body, when heated or cooled (through heat transfer), gains or loses some amount of energy. Based on this, it is customary to call this amount of energy the amount of heat.

So, the amount of heat is the energy that a body gives or receives during the process of heat transfer.

How much heat is needed to heat water? On simple example You can understand that heating different amounts of water will require different amounts of heat. Let's say we take two test tubes with 1 liter of water and 2 liters of water. In which case will more heat be required? In the second, where there are 2 liters of water in a test tube. The second test tube will take longer to heat up if we heat them with the same fire source.

Thus, the amount of heat depends on body mass. The greater the mass, the greater the amount of heat required for heating and, accordingly, the longer it takes to cool the body.

What else does the amount of heat depend on? Naturally, from the difference in body temperatures. But that is not all. After all, if we try to heat water or milk, we will need different amounts of time. That is, it turns out that the amount of heat depends on the substance of which the body consists.

As a result, it turns out that the amount of heat that is needed for heating or the amount of heat that is released when a body cools depends on its mass, on the change in temperature and on the type of substance of which the body is composed.

How is the amount of heat measured?

Behind unit of heat it is generally accepted 1 Joule. Before the advent of the unit of measurement of energy, scientists considered the amount of heat as calories. This unit of measurement is usually abbreviated as “J”

Calorie- this is the amount of heat that is needed to heat 1 gram of water by 1 degree Celsius. The abbreviated form of calorie measurement is “cal”.

1 cal = 4.19 J.

Please note that in these energy units it is customary to note nutritional value food products kJ and kcal.

1 kcal = 1000 cal.

1 kJ = 1000 J

1 kcal = 4190 J = 4.19 kJ

What is specific heat capacity

Each substance in nature has its own properties, and heating each individual substance requires a different amount of energy, i.e. amount of heat.

Specific heat substances- this is a quantity equal to the amount of heat that needs to be transferred to a body with a mass of 1 kilogram in order to heat it to a temperature of 1 0 C

Specific heat capacity is designated by the letter c and has a measurement value of J/kg*

For example, the specific heat capacity of water is 4200 J/kg* 0 C. That is, this is the amount of heat that needs to be transferred to 1 kg of water to heat it by 1 0 C

It should be remembered that the specific heat capacity of substances in different states of aggregation is different. That is, to heat the ice by 1 0 C will require a different amount of heat.

How to calculate the amount of heat to heat a body

For example, it is necessary to calculate the amount of heat that needs to be spent in order to heat 3 kg of water from a temperature of 15 0 C up to temperature 85 0 C. We know the specific heat capacity of water, that is, the amount of energy that is needed to heat 1 kg of water by 1 degree. That is, in order to find out the amount of heat in our case, you need to multiply the specific heat capacity of water by 3 and by the number of degrees by which you want to increase the water temperature. So that's 4200*3*(85-15) = 882,000.

In brackets we calculate the exact number of degrees, subtracting the initial result from the final required result

So, in order to heat 3 kg of water from 15 to 85 0 C, we need 882,000 J of heat.

The amount of heat is denoted by the letter Q, the formula for calculating it is as follows:

Q=c*m*(t 2 -t 1).

Analysis and solution of problems

Problem 1. How much heat is required to heat 0.5 kg of water from 20 to 50 0 C

Given:

m = 0.5 kg.,

s = 4200 J/kg* 0 C,

t 1 = 20 0 C,

t 2 = 50 0 C.

We determined the specific heat capacity from the table.

Solution:

2 -t 1 ).

Substitute the values:

Q=4200*0.5*(50-20) = 63,000 J = 63 kJ.

Answer: Q=63 kJ.

Task 2. What amount of heat is required to heat an aluminum bar weighing 0.5 kg by 85 0 C?

Given:

m = 0.5 kg.,

s = 920 J/kg* 0 C,

t 1 = 0 0 C,

t 2 = 85 0 C.

Solution:

the amount of heat is determined by the formula Q=c*m*(t 2 -t 1 ).

Substitute the values:

Q=920*0.5*(85-0) = 39,100 J = 39.1 kJ.

Answer: Q= 39.1 kJ.

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

During heat exchange, a change in the internal energy of the body occurs. A measure of the 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 a body receives (or gives up) during the process of heat exchange.

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 transition from one type to another (from one body to another) when the state changes and significantly 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 a 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 capacity is 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 weighing 1 kg in order to heat it by 1 K.

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

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

To transform a liquid into steam at a constant temperature, it is necessary to expend an amount of heat

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 impart an amount of heat to the body

where is the specific heat of fusion. When a body crystallizes, the same amount of heat is released.

The amount of heat released during complete combustion of fuel with 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).

The focus of our article is the amount of heat. We will consider the concept of internal energy, which is transformed when this quantity changes. We will also show some examples of the use of calculations in human activity.

Heat

Every person has their own associations with any word in their native language. They are determined personal experience and irrational feelings. What do you usually think of when you hear the word “warmth”? A soft blanket, a working central heating radiator in winter, the first sunlight in spring, a cat. Or a mother’s look, a friend’s comforting word, timely attention.

Physicists mean a very specific term by this. And very important, especially in some sections of this complex but fascinating science.

Thermodynamics

It is not worth considering the amount of heat in isolation from the simplest processes on which the law of conservation of energy is based - nothing will be clear. Therefore, first let us remind our readers of them.

Thermodynamics considers any thing or object as a very large quantity elementary parts - atoms, ions, molecules. Its equations describe any change in the collective state of the system as a whole and as a part of the whole when macroparameters change. The latter refers to temperature (denoted as T), pressure (P), concentration of components (usually C).

Internal energy

Internal energy is a rather complex term, the meaning of which is worth understanding before talking about the amount of heat. It denotes the energy that changes when the value of the macroparameters of an object increases or decreases and does not depend on the reference system. Is a part total energy. It coincides with it in conditions when the center of mass of the thing under study is at rest (that is, there is no kinetic component).

When a person feels that an object (say, a bicycle) has warmed up or cooled down, this indicates that all the molecules and atoms that make up that system have experienced a change in internal energy. However, the constant temperature does not mean the preservation of this indicator.

Work and heat

The internal energy of any thermodynamic system can be transformed in two ways:

by doing work on it;
during heat exchange with the environment.

The formula for this process looks like this:

dU=Q-A, where U is internal energy, Q is heat, A is work.

Let the reader not be deceived by the simplicity of the expression. The rearrangement shows that Q=dU+A, however, the introduction of entropy (S) brings the formula to the form dQ=dSxT.

Since in this case the equation takes the form of a differential one, the first expression requires the same. Next, depending on the forces acting in the object under study and the parameter that is being calculated, the required ratio is derived.

Let's take a metal ball as an example of a thermodynamic system. If you press on it, throw it up, drop it into a deep well, then this means doing work on it. Outwardly, all these harmless actions will not cause any harm to the ball, but its internal energy will change, albeit very slightly.

The second method is heat exchange. Now we come to the main goal of this article: a description of what the amount of heat is. This is a change in the internal energy of a thermodynamic system that occurs during heat exchange (see formula above). It is measured in joules or calories. Obviously, if you hold the ball over a lighter, in the sun, or simply in a warm hand, it will heat up. And then you can use the change in temperature to find the amount of heat that was communicated to him.

Why gas is the best example of a change in internal energy, and why schoolchildren don’t like physics because of this

Above we described changes in the thermodynamic parameters of a metal ball. They are not very noticeable without special devices, and the reader can only take the word about the processes occurring with the object. It's another matter if the system is gas. Press on it - it will be visible, heat it - the pressure will rise, lower it underground - and it can be easily recorded. Therefore, in textbooks, gas is most often used as a visual thermodynamic system.

But, alas, in modern education Not much attention is paid to real experiments. Scientist who writes Toolkit, understands perfectly what is at stake. It seems to him that using the example of gas molecules, all thermodynamic parameters will be properly demonstrated. But a student who is just discovering this world is bored hearing about an ideal flask with a theoretical piston. If the school had real research laboratories and allocated hours to work in them, things would be different. So far, unfortunately, the experiments are only on paper. And, most likely, this is precisely the reason that people consider this branch of physics to be something purely theoretical, far from life and unnecessary.

Therefore, we decided to use the bicycle already mentioned above as an example. A person presses on the pedals and does work on them. In addition to imparting torque to the entire mechanism (thanks to which the bicycle moves in space), the internal energy of the materials from which the levers are made changes. The cyclist presses the handles to turn, and again does the work.

The internal energy of the outer coating (plastic or metal) increases. A person rides out into a clearing under the bright sun - the bicycle heats up, its amount of heat changes. Stops to rest in the shade of an old oak tree and the system cools, losing calories or joules. Increases speed - energy exchange increases. However, calculating the amount of heat in all these cases will show a very small, imperceptible value. Therefore, it seems that the manifestations of thermodynamic physics in real life No.

Application of calculations for changes in the amount of heat

The reader will probably say that all this is very educational, but why are we so tormented at school with these formulas? And now we will give examples in which areas of human activity they are directly needed and how this concerns anyone in their everyday life.

First, look around you and count: how many metal objects surround you? Probably more than ten. But before becoming a paper clip, a carriage, a ring or a flash drive, any metal undergoes smelting. Every plant that processes, say, iron ore, must understand how much fuel is required in order to optimize costs. And when calculating this, it is necessary to know the heat capacity of the metal-containing raw material and the amount of heat that needs to be imparted to it in order for all technological processes to occur. Since the energy released by a unit of fuel is calculated in joules or calories, the formulas are needed directly.

Or another example: most supermarkets have a department with frozen goods - fish, meat, fruit. Where raw materials from animal meat or seafood are transformed into semi-finished products, they must know how much electricity refrigeration and freezing units will consume per ton or unit of finished product. To do this, you need to calculate how much heat a kilogram of strawberries or squid loses when cooled by one degree Celsius. And in the end, this will show how much electricity a freezer of a certain power will consume.

Planes, ships, trains

Above we showed examples of relatively motionless, static objects to which a certain amount of heat is imparted or from which, on the contrary, a certain amount of heat is taken away. For objects that move in conditions of constantly changing temperature during operation, calculations of the amount of heat are important for another reason.

There is such a thing as “metal fatigue”. It also includes maximum permissible loads at a certain rate of temperature change. Imagine an airplane taking off from the humid tropics into the frozen upper atmosphere. Engineers have to work hard to ensure that it does not fall apart due to cracks in the metal that appear when the temperature changes. They are looking for an alloy composition that can withstand real loads and have a large margin of safety. And in order not to search blindly, hoping to accidentally stumble upon the desired composition, you have to do a lot of calculations, including those that include changes in the amount of heat.

Learning Objective: Introduce the concepts of heat quantity and specific heat capacity.

Developmental goal: To cultivate attentiveness; teach to think, draw conclusions.

1. Updating the topic

2. Explanation of new material. 50 min.

You already know that the internal energy of a body can change both by doing work and by heat transfer (without doing work).

The energy that a body gains or loses during heat transfer is called the amount of heat. (write in notebook)

This means that the units for measuring the amount of heat are also Joules ( J).

We conduct an experiment: two glasses in one with 300 g of water, and in the other 150 g, and an iron cylinder weighing 150 g. Both glasses are placed on the same tile. After some time, thermometers will show that the water in the vessel in which the body is located heats up faster.

This means that heating 150 g of iron requires less heat than heating 150 g of water.

The amount of heat transferred to a body depends on the type of substance from which the body is made. (write in notebook)

We propose the question: is the same amount of heat required to heat bodies of equal mass, but consisting of different substances, to the same temperature?

We conduct an experiment with Tyndall's device to determine specific heat capacity.

We conclude: bodies made of different substances, but of the same mass, give up when cooled and require different amounts of heat when heated by the same number of degrees.

We draw conclusions:

1. To heat bodies of equal mass, consisting of different substances, to the same temperature, it is required different quantity warmth.

2. Bodies of equal mass, consisting of different substances and heated to the same temperature. When cooled by the same number of degrees, different amounts of heat are released.

We conclude that the amount of heat required to heat a unit mass of different substances by one degree will vary.

We give the definition of specific heat capacity.

A physical quantity numerically equal to the amount of heat that must be transferred to a body weighing 1 kg in order for its temperature to change by 1 degree is called the specific heat capacity of a substance.

Enter the unit of measurement for specific heat capacity: 1J/kg*degree.

Physical meaning of the term : Specific heat capacity shows by what amount the internal energy of 1g (kg) of a substance changes when it is heated or cooled by 1 degree.

Let's look at the table of specific heat capacities of some substances.

We solve the problem analytically

How much heat is required to heat a glass of water (200 g) from 20 0 to 70 0 C.

To heat 1 g per 1 g, 4.2 J is required.

And to heat 200 g by 1 g it will take 200 more - 200 * 4.2 J.

And to heat 200 g by (70 0 -20 0) it will take another (70-20) more - 200 * (70-20) * 4.2 J

Substituting the data, we get Q = 200 * 50 * 4.2 J = 42000 J.

Let us write the resulting formula in terms of the corresponding quantities

4. What determines the amount of heat received by a body when heated?

Please note that the amount of heat required to heat any body is proportional to the mass of the body and the change in its temperature.,

There are two cylinders of equal mass: iron and brass. Is the same amount of heat required to heat them the same number of degrees? Why?

What amount of heat is needed to heat 250 g of water from 20 o to 60 0 C.

What is the relationship between calorie and joule?

A calorie is the amount of heat required to heat 1 g of water by 1 degree.

1 cal = 4.19 = 4.2 J

1kcal=1000cal

1kcal=4190J=4200J

3. Problem solving. 28 min.

If cylinders of lead, tin and steel weighing 1 kg heated in boiling water are placed on ice, they will cool and part of the ice under them will melt. How will the internal energy of the cylinders change? Under which cylinder will it melt? more ice, under which – less?

A heated stone weighing 5 kg. Cooling in water by 1 degree, it transfers 2.1 kJ of energy to it. What is the specific heat capacity of the stone?

When hardening a chisel, it was first heated to 650 0, then lowered into oil, where it cooled to 50 0 C. What amount of heat was released if its mass was 500 grams.

How much heat was used to heat a steel blank for the compressor crankshaft weighing 35 kg from 20 0 to 1220 0 C.

Independent work

What type of heat transfer?

Students fill out the table.

The air in the room is heated through the walls.
Through open window, into which warm air enters.
Through glass that lets in the sun's rays.
The earth is heated by the sun's rays.
The liquid is heated on the stove.
The steel spoon is heated by the tea.
The air is heated by the candle.
The gas moves near the fuel-generating parts of the machine.
Heating a machine gun barrel.
Boiling milk.

5. Homework: Peryshkin A.V. “Physics 8” § §7, 8; collection of problems 7-8 Lukashik V.I. No. 778-780, 792,793 2 min.