How much warmth. The formula for the amount of heat

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

Developmental goal: To cultivate mindfulness; learn to think, draw conclusions.

1. Topic update

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 transferring heat (without doing work).

The energy that a body receives or loses during heat transfer is called the amount of heat. (notebook entry)

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

We conduct an experiment: two glasses in one 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 less iron is needed to heat 150 g of iron. quantity of heat than for heating 150 g of water.

The amount of heat transferred to the body depends on the kind of substance from which the body is made. (notebook entry)

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 the Tyndall device to determine the specific heat capacity.

We conclude: bodies of different substances, but of the same mass, give off when cooled and demand when heated by the same number of degrees different amount warmth.

We draw conclusions:

1. To heat bodies of equal mass, consisting of different substances, to the same temperature, a different amount of heat is required.

2. Bodies of equal mass, consisting of different substances and heated to the same temperature. When cooled by the same number of degrees, they give off a different amount of heat.

We make the conclusion that the amount of heat required to raise one degree of unit mass of different substances will be different.

We give the definition of specific heat capacity.

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

We introduce the unit of measurement of specific heat capacity: 1J / kg * degree.

The physical meaning of the term : specific heat capacity shows how much the internal energy of 1 g (kg.) of a substance changes when it is heated or cooled by 1 degree.

Consider 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.

For heating 1 g per 1 g. Required - 4.2 J.

And to heat 200 g per 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.

We write the resulting formula in terms of the corresponding quantities

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

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

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

How much heat is needed to heat 250 g of water from 20 o to 60 0 C.

What is the relationship between calories and joules?

A calorie is the amount of heat required to raise the temperature of 1 gram 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 heated in boiling water with a mass of 1 kg 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 of the cylinders will melt more ice, under which - less?

A heated stone with a mass of 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 g.

How much heat was spent on heating from 20 0 to 1220 0 C. a steel billet for the crankshaft of a compressor weighing 35 kg.

Independent work

What type of heat transfer?

Students complete the table.

1. The air in the room is heated through the walls.
2. Through an open window into which warm air enters.
3. Through glass, which transmits the rays of the sun.
4. The earth is heated by the rays of the sun.
5. The liquid is heated on the stove.
6. The steel spoon is heated by the tea.
7. The air is heated by a candle.
8. The gas moves around the heat-producing parts of the machine.
9. Heating the barrel of a machine gun.
10. Boiling milk.

5. Homework: Peryshkin A.V. “Physics 8” §§7, 8; collection of tasks 7-8 Lukashik V.I. Nos. 778-780, 792,793 2 min.

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 exchange, there is a change internal energy body. 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 point, 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).

What heats up faster on the stove - a kettle or a bucket of water? The answer is obvious - a kettle. Then the second question is why?

The answer is no less obvious - because the mass of water in the kettle is less. Great. And now you can do the most real physical experience yourself at home. To do this, you will need two identical small saucepans, an equal amount of water and vegetable oil, for example, half a liter and a stove. Put pots of oil and water on the same fire. And now just watch what will heat up faster. If there is a thermometer for liquids, you can use it, if not, you can just try the temperature from time to time with your finger, just be careful not to burn yourself. In any case, you will soon see that the oil heats up significantly faster than water. And one more question, which can also be implemented in the form of experience. What will boil faster - warm water or cold? Everything is obvious again - the warm one will be the first to finish. Why all these strange questions and experiments? In order to define physical quantity, called "the amount of heat".

Quantity of heat

The amount of heat is the energy that the body loses or gains during heat transfer. This is clear from the name. When cooling, the body will lose a certain amount of heat, and when heated, it will absorb. And the answers to our questions showed us what does the amount of heat depend on? First, than more weight body, the more heat must be expended to change its temperature by one degree. Secondly, the amount of heat necessary to heat a body depends on the substance of which it is composed, that is, on the kind of substance. And thirdly, the difference in body temperature before and after heat transfer is also important for our calculations. Based on the foregoing, we can determine the amount of heat by the formula:

Q=cm(t_2-t_1) ,

where Q is the amount of heat,
m- body mass,
(t_2-t_1) - difference between initial and final body temperatures,
c - specific heat capacity of the substance, is found from the relevant tables.

Using this formula, you can calculate the amount of heat that is necessary to heat any body or that this body will release when it cools.

The amount of heat is measured in joules (1 J), like any other form of energy. However, this value was introduced not so long ago, and people began to measure the amount of heat much earlier. And they used a unit that is widely used in our time - a calorie (1 cal). 1 calorie is the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius. Guided by these data, lovers of counting calories in the food they eat can, for the sake of interest, calculate how many liters of water can be boiled with the energy that they consume with food during the day.

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

Each body, when heated or cooled (during heat transfer), receives 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 in the process of heat transfer.

How much heat is needed to heat water? On simple example It can be understood that different amounts of heat are required to heat different amounts of water. Suppose 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 the mass of the body. The greater the mass, the greater the amount of heat required for heating and, accordingly, the cooling of the body takes more time.

What else determines the amount of heat? Naturally, from the temperature difference of the bodies. But that is not all. After all, if we try to heat water or milk, we will need a different amount 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 the body cools depends on its mass, on temperature changes and on the type of substance that the body consists of.

How is the amount of heat measured?

Behind unit of heat considered to be 1 Joule. Before the advent of the unit of measurement of energy, scientists considered the amount of heat in calories. It is customary to write this unit of measurement in abbreviated form - “J”

Calorie is the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius. The abbreviated unit of calorie is usually written - "cal".

1 cal = 4.19 J.

Please note that in these units of energy it is customary to note nutritional value food 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 capacity of a substance is a quantity equal to the amount of heat that must be transferred to a body with a mass of 1 kilogram in order to heat it to a temperature of 1 0C

Specific heat capacity is denoted 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 in order to heat it by 1 0C

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

How to calculate the amount of heat to heat the 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 to 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 need to increase the temperature of the water. So this is 4200*3*(85-15) = 882,000.

In parentheses, we calculate exact amount degrees, subtracting from the final required result the initial

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 its calculation is as follows:

Q \u003d c * m * (t 2 -t 1).

Parsing and solving problems

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

Given:

m = 0.5 kg.,

c \u003d 4200 J / kg * 0 C,

t 1 \u003d 20 0 C,

t 2 \u003d 50 0 C.

the value specific heat we determined from the table.

Solution:

2 -t 1 ).

Substitute the values:

Q \u003d 4200 * 0.5 * (50-20) \u003d 63,000 J \u003d 63 kJ.

Answer: Q=63 kJ.

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

Given:

m = 0.5 kg.,

c \u003d 920 J / kg * 0 C,

t 1 \u003d 0 0 С,

t 2 \u003d 85 0 C.

Solution:

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

Substitute the values:

Q \u003d 920 * 0.5 * (85-0) \u003d 39 100 J \u003d 39.1 kJ.

Answer: Q= 39.1 kJ.

The internal energy of a body depends on its temperature and external conditions - volume, etc. If external conditions remain unchanged, i.e., the volume and other parameters are constant, then the internal energy of the body depends only on its temperature.

It is possible to change the internal energy of a body not only by heating it in a flame or by performing mechanical work on it (without changing the position of the body, for example, the work of the friction force), but also by bringing it into contact with another body that has a temperature different from the temperature of this body, i.e., through heat transfer.

The amount of internal energy that a body gains or loses in the process of heat transfer is called the “amount of heat”. The amount of heat is usually denoted by the letter `Q`. If the internal energy of the body in the process of heat transfer increases, then the heat is assigned a plus sign, and the body is said to have been given heat `Q`. With a decrease in internal energy in the process of heat transfer, heat is considered negative, and it is said that the amount of heat `Q` has been taken (or removed) from the body.

The amount of heat can be measured in the same units in which mechanical energy is measured. In SI it is `1` joule. There is another unit of heat measurement - calorie. Calorie is the amount of heat required to heat `1` g of water by `1^@ bb"C"`. The ratio between these units was established by Joule: `1` cal `= 4.18` J. This means that due to work in `4.18` kJ, the temperature of `1` kilogram of water will increase by `1` degree.

The amount of heat required to heat the body by `1^@ bb"C"` is called the heat capacity of the body. The heat capacity of a body is denoted by the letter `C`. If the body was given a small amount of `Delta Q` heat, and the body temperature changed by `Delta t` degrees, then

If the body is surrounded by a shell that conducts heat poorly, then the temperature of the body, if left to itself, will remain practically constant for a long time. Such ideal shells, of course, do not exist in nature, but shells can be created that approach these in their properties.

Examples are cladding spaceships, Dewar vessels used in physics and technology. The Dewar vessel is a glass or metal container with double mirrored walls, between which a high vacuum is created. The glass flask of a home thermos is also a Dewar vessel.

The shell is insulating calorimeter- a device that measures the amount of heat. The calorimeter is a large thin-walled glass, placed on pieces of cork inside another large glass so that a layer of air remains between the walls, and closed from above with a heat-resistant lid.

If in the calorimeter two or more bodies with various temperatures, and wait, then after a while inside the calorimeter will be established thermal equilibrium. In the process of transition to thermal equilibrium, some bodies will give off heat (the total amount of heat `Q_(sf"otd")`), others will receive heat (the total amount of heat `Q_(sf"floor")`). And since the calorimeter and the bodies contained in it do not exchange heat with the surrounding space, but only between themselves, we can write the relation, also called heat balance equation:

In a number of thermal processes, heat can be absorbed or released by a body without changing its temperature. Such thermal processes take place when the aggregate state of a substance changes - melting, crystallization, evaporation, condensation and boiling. Let us briefly dwell on the main characteristics of these processes.

Melting- the process of transformation of a crystalline solid into a liquid. The melting process takes place at constant temperature, heat is absorbed.

The specific heat of fusion `lambda` is equal to the amount of heat required to melt `1` kg of a crystalline substance taken at the melting point. The amount of heat `Q_(sf"pl")`, which is required to transfer a solid body of mass `m` at a melting point into a liquid state, is equal to

Since the melting temperature remains constant, the amount of heat imparted to the body goes to increase the potential energy of molecular interaction, and the crystal lattice is destroyed.

Process crystallization is the reverse process of melting. During crystallization, the liquid turns into a solid body and the amount of heat is released, which is also determined by formula (1.5).

Evaporation is the process of converting liquid into vapor. Evaporation occurs from the open surface of the liquid. In the process of evaporation, the fastest molecules leave the liquid, i.e., molecules that can overcome the forces of attraction from the molecules of the liquid. As a result, if the liquid is thermally insulated, then in the process of evaporation it cools.

The specific heat of vaporization `L` is equal to the amount of heat required to turn `1` kg of liquid into steam. The amount of heat `Q_(sf"isp")`, which is required to convert a liquid of mass `m` into a vapor state is equal to

Condensation is a process that is the reverse of evaporation. When condensed, the vapor turns into a liquid. This releases heat. The amount of heat released during the condensation of steam is determined by formula (1.6).

Boiling is a process in which the pressure saturated vapors liquid equals atmospheric pressure, therefore, evaporation occurs not only from the surface, but also throughout the volume (there are always air bubbles in the liquid, when boiling, the vapor pressure in them reaches atmospheric pressure, and the bubbles rise up).