Along with mechanical energy, any body (or system) has internal energy. Internal energy is the energy of rest. It consists of the thermal chaotic movement of the molecules that make up the body, their potential energy relative position, kinetic and potential energy of electrons in atoms, nucleons in nuclei, and so on.
In thermodynamics, it is important to know not the absolute value of internal energy, but its change.
IN thermodynamic processes only the kinetic energy of moving molecules changes (thermal energy is not enough to change the structure of an atom, much less a nucleus). Therefore, in fact under internal energy in thermodynamics we mean energy thermal chaotic molecular movements.
Internal energy U one mole of an ideal gas is equal to:
Thus, internal energy depends only on temperature. The internal energy U is a function of the state of the system, regardless of background.
It is clear that in general case a thermodynamic system can have both internal and mechanical energy, and different systems can exchange these types of energy.
Exchange mechanical energy characterized by perfect work A, and the exchange of internal energy – the amount of heat transferred Q.
For example, in winter you threw a hot stone into the snow. Due to the reserve of potential energy, the mechanical work by crushing the snow, and due to the reserve of internal energy, the snow was melted. If the stone was cold, i.e. If the temperature of the stone is equal to the temperature of the medium, then only work will be done, but there will be no exchange of internal energy.
So, work and heat are not special forms of energy. We cannot talk about the reserve of heat or work. This measure of transferred another system of mechanical or internal energy. We can talk about the reserve of these energies. In addition, mechanical energy can be converted into thermal energy and back. For example, if you hit an anvil with a hammer, then after a while the hammer and the anvil will heat up (this is an example dissipation energy).
We can give many more examples of the transformation of one form of energy into another.
Experience shows that in all cases, The transformation of mechanical energy into thermal energy and vice versa always occurs in strictly equivalent quantities. This is the essence of the first law of thermodynamics, which follows from the law of conservation of energy.
The amount of heat imparted to the body goes to increase internal energy and to perform work on the body:
| , | (4.1.1) |
- That's what it is first law of thermodynamics , or law of conservation of energy in thermodynamics.
Sign rule: if heat is transferred from environment this system, and if the system performs work on surrounding bodies, in this case . Taking into account the sign rule, the first law of thermodynamics can be written as:
In this expression U– system state function; d U is its total differential, and δ Q and δ A they are not. In each state, the system has a certain and only this value of internal energy, so we can write:
 ,
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It is important to note that heat Q and work A depend on how the transition from state 1 to state 2 is accomplished (isochorically, adiabatically, etc.), and the internal energy U does not depend. At the same time, it cannot be said that the system has a certain this state the meaning of heat and work.
From formula (4.1.2) it follows that the amount of heat is expressed in the same units as work and energy, i.e. in joules (J).
Of particular importance in thermodynamics are circular or cyclic processes in which a system, after passing through a series of states, returns to its original state. Figure 4.1 shows the cyclic process 1– A–2–b–1, while work A was done.
Rice. 4.1
Because U is a state function, then
| (4.1.3) |
This is true for any state function.
If then according to the first law of thermodynamics, i.e. It is impossible to build a periodically operating engine that would perform more work than the amount of energy imparted to it from the outside. In other words, perpetual motion machine the first kind is impossible. This is one of the formulations of the first law of thermodynamics.
It should be noted that the first law of thermodynamics does not indicate in which direction the processes of state change occur, which is one of its shortcomings.
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.
Ability to calculate required amount warmth 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 let's write down 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. According to the table 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 
.
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 |
The internal energy of a thermodynamic system can be changed in two ways:
- doing over system work,
- using thermal interaction.
The transfer of heat to a body is not associated with the performance of macroscopic work on the body. IN in this case The change in internal energy is caused by the fact that individual molecules of a body with a higher temperature do work on some molecules of a body that has a lower temperature. In this case, thermal interaction is realized due to thermal conductivity. Energy transfer is also possible using radiation. The system of microscopic processes (relating 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 is the energy that is received (or given up) by a body in the process of heat exchange with surrounding bodies (environment). The symbol for heat is usually 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 transferred to the system (body), or it can be taken from it. It is believed that if heat is transferred to the system, then it is positive.
Formula for calculating heat when temperature changes
We denote the elementary amount of heat as . Let us note that the element of heat that the system receives (gives) with a small change in its state is not a complete 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 imparted to the system, and the temperature changes from T to T+dT, is equal to:
where C is the heat capacity of the body. If the body in question is homogeneous, then formula (1) for the amount of heat can be represented as:
where is the specific heat capacity of the body, m – body mass, - 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 an amount can be calculated as:
where t 2, t 1 body temperatures before and after heating. Please note that when finding the difference () in calculations, temperatures can be substituted both in degrees Celsius and in kelvins.
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 phase transition.
So, to transfer an element of matter from the state solid into the liquid he should impart an amount of heat () equal to:
Where - specific heat melting, dm – element of body mass. 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 evaporation) required to convert liquid into vapor can be found as:
where r is the specific heat of evaporation. When steam condenses, heat is released. The heat of evaporation is equal to the heat of condensation of equal masses of substance.
Units for measuring the amount of heat
The basic unit of measurement for the amount of heat in the SI system is: [Q]=J
An extra-system unit of heat, which 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 is t 1 = 10 C, the temperature of the second mass of water is t 2 = 60 C?
Solution. Let us write the heat balance equation in the form:
where Q=cmt is the amount of heat prepared after mixing the water; Q 1 = cm 1 t 1 - the amount of heat of a part of water with temperature t 1 and mass m 1; Q 2 = cm 2 t 2 - the amount of heat of a part of water with temperature t 2 and mass m 2.
From equation (1.1) it follows:
When combining cold (V 1) and hot (V 2) parts of water into a single volume (V), we can assume that:
So, we get a system of equations:
Having solved it we get:
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 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 significantly faster than water. And one more question, which can also be implemented in the form of experience. Which 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) - difference between 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, just for fun, calculate how many liters of water can be boiled with the energy they consume with food during the day.
As is known, at different 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.
