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 the 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 a certain 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 perform mechanical work to push the stopper out of the 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 from the lighting network can be supplied. 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. Electric current 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. In the process of heating the liquid in various 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 thermocouple junction is lowered into a vessel with cold water to ensure its constant temperature. The other thermocouple junction measures the temperature of the liquid under study).
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 directly proportional relationship between them. 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 the melting of solids, vaporization of liquids, and 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.
As we already know, the internal energy of a body can change both when doing work and through heat transfer (without doing work).
The main difference between work and the amount of heat is that work determines the process of converting the internal energy of the system, which is accompanied by the transformation of energy from one type to another. In the event that a change in internal energy occurs with the help of heat transfer , the transfer of energy from one body to another is carried out due to thermal conductivity , radiation, or.
convection The energy that a body loses or gains during heat transfer is called
When calculating the amount of heat, you need to know what quantities influence it.
We will heat two vessels using two identical burners. One vessel contains 1 kg of water, the other contains 2 kg. The temperature of the water in the two vessels is initially the same. We can see that during the same time, the water in one of the vessels heats up faster, although both vessels receive an equal amount of heat.
Thus, we conclude: the greater the mass of a given body, the greater the amount of heat that must be expended in order to lower or increase its temperature by the same number of degrees.
When a body cools down, it gives off a greater amount of heat to neighboring objects, the greater its mass.
We all know that if we need to heat a full kettle of water to a temperature of 50°C, we will spend less time on this action than to heat a kettle with the same volume of water, but only to 100°C. In case number one, less heat will be given to the water than in case two.
Thus, the amount of heat required for heating directly depends on whether how many degrees the body can warm up. We can conclude: the amount of heat directly depends on the difference in body temperature.
But is it possible to determine the amount of heat required not to heat water, but some other substance, say, oil, lead or iron?
Fill one vessel with water and fill the other with vegetable oil. The masses of water and oil are equal. We will heat both vessels evenly on identical burners. Let's start the experiment at equal initial temperatures of vegetable oil and water. Five minutes later, having measured the temperatures of the heated oil and water, we will notice that the temperature of the oil is much higher than the temperature of the water, although both liquids received the same amount of heat.
The obvious conclusion is: When heating equal masses of oil and water at the same temperature, different amounts of heat are required.
And we immediately draw another conclusion: the amount of heat required to heat a body directly depends on the substance of which the body itself consists (the type of substance).
Thus, the amount of heat needed to heat a body (or released when cooling) directly depends on the mass of the body, the variability of its temperature, and the type of substance.
The quantity of heat is denoted by the symbol Q. Like other different types of energy, the quantity of heat is measured in joules (J) or kilojoules (kJ).
1 kJ = 1000 J
However, history shows that scientists began to measure the amount of heat long before the concept of energy appeared in physics. At that time, a special unit was developed for measuring the amount of heat - calorie (cal) or kilocalorie (kcal). The word has Latin roots, calor - heat.
1 kcal = 1000 cal
Calorie– this is the amount of heat needed to heat 1 g of water by 1°C
1 cal = 4.19 J ≈ 4.2 J
1 kcal = 4190 J ≈ 4200 J ≈ 4.2 kJ
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In this lesson we will learn how to calculate the amount of heat required to heat a body or released by it when cooling. To do this, we will summarize the knowledge that was acquired in previous lessons.
In addition, we will learn, using 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 when cooled.
The ability to calculate the required amount of heat is very important. This may be needed, for example, when calculating the amount of heat that needs to be imparted to water to heat a room.
Rice. 1. The amount of heat that must be imparted 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
This knowledge is also needed, for example, to determine the amount of heat that is released by the Sun and falls on 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 using a scale);
- the temperature difference by which a body must be heated or cooled (usually measured using 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 by which the amount of heat is calculated looks like this:
The following quantities appear in this formula:
The amount of heat measured in joules (J);
The specific heat capacity of a substance is measured in ;
- temperature difference, measured in degrees Celsius ().
Let's consider the problem of calculating the amount of heat.
Task
A copper glass with a mass of grams contains water with a volume of liter at a temperature. How much heat must be transferred to a glass of water so that its temperature becomes equal to ?
Rice. 5. Illustration of the problem conditions
First we write down a short condition ( Given) and convert all quantities to the international system (SI).
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Given: |
SI |
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Find: |
Solution:
First, determine what other quantities we need to solve this problem. Using 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 to calculate the amount of heat we need a mass of water. According to the condition, we are given only the volume. Therefore, from the table we take the density of water: (Table 2).
Table 1. Specific heat capacity of some substances,
Table 2. Densities of some liquids
Now we have everything we need to solve this problem.
Note that the final 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:
Let's first calculate the amount of heat required to heat a copper glass:
Before calculating the amount of heat required to heat water, let’s calculate the mass of water using a formula that is familiar to us from grade 7:
Now we can calculate:
Then we can calculate:
Let's remember what kilojoules mean. The prefix “kilo” means, that is.
Answer:.
For the convenience of solving problems of finding the amount of heat (the so-called direct problems) and quantities associated with this concept, you can use the following table.
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Required quantity |
Designation |
Units |
Basic formula |
Formula for quantity |
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Quantity of heat |
In the next lesson we will conduct laboratory work, the purpose of which is to learn how to experimentally determine the specific heat capacity of a solid. Listliterature:
Homework |
What will heat up faster on the stove - a kettle or a bucket of water? The answer is obvious - a teapot. 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 a 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 each and a stove. Place saucepans with oil and water on the same heat. Now just watch what will heat up faster. If you have a thermometer for liquids, you can use it; if not, you can simply test the temperature with your finger from time to time, just be careful not to get burned. In any case, you will soon see that the oil heats up much 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 first at the finish line. Why all these strange questions and experiments? To determine the physical quantity called “amount of heat”.
Quantity of heat
The amount of heat is the energy that a 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 heating, it will absorb. And the answers to our questions showed us What does the amount of heat depend on? Firstly, the greater the mass of a body, the greater the amount of heat that must be expended to change its temperature by one degree. Secondly, the amount of heat required to heat a body depends on the substance of which it consists, that is, on the type of substance. And thirdly, the difference in body temperature before and after heat transfer is also important for our calculations. Based on the above, we can determine the amount of heat using the formula:
Q=cm(t_2-t_1) ,
where Q is the amount of heat,
m - body weight,
(t_2-t_1) - the difference between the initial and final body temperatures,
c is the specific heat capacity of the substance, found from the corresponding 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 cooling.
The amount of heat is measured in joules (1 J), like any type of energy. However, this value was introduced not so long ago, and people began measuring the amount of heat much earlier. And they used a unit that is widely used in our time - calorie (1 cal). 1 calorie is the amount of heat required to heat 1 gram of water by 1 degree Celsius. Guided by these data, those who like to count calories in the food they eat can, for fun, calculate how many liters of water can be boiled with the energy they consume with food during the day.
HEAT EXCHANGE.
1. Heat exchange.
Heat exchange or heat transfer is the process of transferring the internal energy of one body to another without doing work.
There are three types of heat transfer.
1) Thermal conductivity- This is heat exchange between bodies during their direct contact.
2) Convection- This is heat exchange in which heat is transferred by gas or liquid flows.
3) Radiation– This is heat exchange through electromagnetic radiation.
2. Amount of heat.
The amount of heat is a measure of the change in the internal energy of a body during heat exchange. Denoted by the letter Q.
Unit for measuring the amount of heat = 1 J.
The amount of heat received by a body from another body as a result of heat exchange can be spent on increasing temperature (increasing the kinetic energy of molecules) or changing the state of aggregation (increasing potential energy).
3.Specific heat capacity of the substance.
Experience shows that the amount of heat required to heat a body of mass m from temperature T 1 to temperature T 2 is proportional to the mass of the body m and the temperature difference (T 2 - T 1), i.e.
Q = cm(T 2 - T 1 ) = smΔ T,
With is called the specific heat capacity of the substance of the heated body.
The specific heat capacity of a substance is equal to the amount of heat that must be imparted to 1 kg of the substance to heat it by 1 K.
Unit of measurement of specific heat capacity =.
The heat capacity values for various substances can be found in physical tables.
Exactly the same amount of heat Q will be released when the body is cooled by ΔT.
4.Specific heat of vaporization.
Experience shows that the amount of heat required to convert a liquid into steam is proportional to the mass of the liquid, i.e.
Q = Lm,
where is the proportionality coefficient L is called the specific heat of vaporization.
The specific heat of vaporization is equal to the amount of heat required to convert 1 kg of liquid at boiling point into steam.
A unit of measurement for the specific heat of vaporization.
During the reverse process, steam condensation, heat is released in the same amount that was spent on steam formation.
5.Specific heat of fusion.
Experience shows that the amount of heat required to transform a solid into a liquid is proportional to the mass of the body, i.e.
Q = λ m,
where the proportionality coefficient λ is called the specific heat of fusion.
The specific heat of fusion is equal to the amount of heat that is necessary to transform a solid body weighing 1 kg into a liquid at the melting point.
A unit of measurement for the specific heat of fusion.
During the reverse process, crystallization of the liquid, heat is released in the same amount that was spent on melting.
6. Specific heat of combustion.
Experience shows that the amount of heat released during complete combustion of fuel is proportional to the mass of the fuel, i.e.
Q = qm,
Where the proportionality coefficient q is called the specific heat of combustion.
The specific heat of combustion is equal to the amount of heat released during complete combustion of 1 kg of fuel.
Unit of measurement of specific heat of combustion.
7. Heat balance equation.
Heat exchange involves two or more bodies. Some bodies give off heat, while others receive it. Heat exchange occurs until the temperatures of the bodies become equal. According to the law of conservation of energy, the amount of heat that is given out is equal to the amount that is received. On this basis, the heat balance equation is written.
Let's look at an example.
A body of mass m 1, the heat capacity of which is c 1, has a temperature T 1, and a body of mass m 2, the heat capacity of which is c 2, has a temperature T 2. Moreover, T 1 is greater than T 2. These bodies are brought into contact. Experience shows that a cold body (m 2) begins to heat up, and a hot body (m 1) begins to cool. This suggests that part of the internal energy of the hot body is transferred to the cold one, and the temperatures are equalized. Let us denote the final overall temperature by θ.
The amount of heat transferred from a hot body to a cold one
Q transferred. = c 1 m 1 (T 1 – θ )
The amount of heat received by a cold body from a hot one
Q received. = c 2 m 2 (θ – T 2 )
According to the law of conservation of energy Q transferred. = Q received., i.e.
c 1 m 1 (T 1 – θ )= c 2 m 2 (θ – T 2 )
Let's open the brackets and express the value of the total steady-state temperature θ.
In this case, we obtain the temperature value θ in kelvins.
However, since Q is passed in the expressions.
and Q is received. is the difference between two temperatures, and it is the same both in Kelvin and in degrees Celsius, then the calculation can be carried out in degrees Celsius. Then
The equalization of temperatures as a result of thermal conductivity can be explained on the basis of molecular kinetic theory as the exchange of kinetic energy between molecules upon collision in the process of thermal chaotic motion.
This example can be illustrated with a graph.