The internal energy of a body depends on its temperature and external conditions - volume, etc. If external conditions remain unchanged, i.e. volume and other parameters are constant, then the internal energy of the body depends only on its temperature.
You can change the internal energy of a body not only by heating it in a flame or performing mechanical work on it (without changing the position of the body, for example, the work of friction), but also by bringing it into contact with another body that has a temperature different from the temperature given body, i.e. through heat transfer.
The amount of internal energy that a body gains or loses during heat transfer is called the “amount of heat.” The amount of heat is usually denoted by the letter `Q`. If the internal energy of a body increases during the process of heat transfer, then the heat is assigned a plus sign, and the body is said to have been given heat `Q`. When the internal energy decreases during the process of heat transfer, the heat is considered negative, and it is said that the amount of heat `Q` has been removed (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 - the calorie. Calorie is the amount of heat required to heat `1` g of water by `1^@ bb"C"`. The relationship between these units was established by Joule: `1` cal `= 4.18` J. This means that due to the work of `4.18` kJ, the temperature of `1` kilogram of water will increase by `1` degree.
The amount of heat required to heat a body by `1^@ bb"C"` is called the heat capacity of the body. The heat capacity of a body is designated by the letter `C`. If the body is given a small amount of heat `Delta Q`, and the body temperature changes to `Delta t` degrees, then
| `Q=C*Deltat=C*(t_2 - t_1)=c*m*(t_2 - t_1)`. | (1.3) |
If a body is surrounded by a shell that does not conduct heat well, then the temperature of the body, if left to its own devices, will remain practically constant for a long time. Such ideal shells, of course, do not exist in nature, but it is possible to create shells that are close to such in their properties.
Examples include cladding spaceships, Dewar vessels used in physics and technology. A Dewar flask is a glass or metal cylinder with double mirror walls, between which a high vacuum is created. The glass flask of a home thermos is also a Dewar flask.
The shell is insulating calorimeter- a device that allows you to measure 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 on top with a heat-insulating lid.
If two or more bodies having different temperatures are brought into thermal contact in a calorimeter and wait, then after some time thermal equilibrium will be established inside the calorimeter. In the process of transition to thermal equilibrium, some bodies will give off heat (total amount of heat `Q_(sf"floor")`), others will receive heat (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 with each other, we can write down a relationship, 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 occur when the aggregate state of a substance changes - melting, crystallization, evaporation, condensation and boiling. Let us briefly look at the main characteristics of these processes.
Melting- the process of turning a crystalline solid into a liquid. The melting process occurs at a constant temperature, while 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 its melting point. The amount of heat `Q_(sf"pl")` that is required to convert a solid body of mass `m` at the melting point into a liquid state is equal to
Since the melting point remains constant, the amount of heat imparted to the body goes to increase the potential energy of interaction between molecules, and the crystal lattice is destroyed.
Process crystallization- This is a process reverse to the melting process. During crystallization, the liquid turns into a solid and an amount of heat is released, also determined by formula (1.5).
Evaporation is the process of converting liquid into vapor. Evaporation occurs from the open surface of the liquid. During the process of evaporation, the fastest molecules leave the liquid, i.e., molecules that can overcome the attractive forces exerted by the liquid molecules. As a result, if the liquid is thermally insulated, it cools during the evaporation process.
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"use")` that is required to convert a liquid of mass `m` into a vapor state is equal to
| `Q_(sf"isp") =L*m`. | (1.6) |
Condensation- a process reverse to the evaporation process. When condensation occurs, steam turns into liquid. This generates heat. The amount of heat released during steam condensation is determined by formula (1.6).
Boiling- a process in which the saturated vapor pressure of a liquid is equal to atmospheric pressure, so evaporation occurs not only from the surface, but throughout the entire volume (there are always air bubbles in the liquid; when boiling, the vapor pressure in them reaches atmospheric pressure, and the bubbles rise upward).
« Physics - 10th grade"
In what processes do aggregate transformations of matter occur?
How can you change the state of aggregation of a substance?
You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
So, when forging a metal, work is done and it heats up, 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 therefore 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, the interaction of slowly moving molecules of a cold body with fast moving molecules of a hot body occurs. As a result, the kinetic energies of the molecules are equalized and the speeds of the molecules of the cold body increase, and those of the hot body decrease.
During heat exchange, energy is not converted from one form to another; part of the internal energy of a more heated body is transferred to a less heated body.
Amount of heat and heat capacity.
You already know that in order to heat a body of mass m from temperature t 1 to temperature t 2, it is necessary to transfer an amount of heat to it:
Q = cm(t 2 - t 1) = cm Δt. (13.5)
When a 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 quantity numerically equal to the amount of heat that a substance weighing 1 kg receives or releases when its temperature changes by 1 K.
The specific heat capacity of gases depends on the process by which heat transfer occurs. 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 solids expand slightly when heated. Their specific heat capacities at constant volume and constant pressure differ little.
Specific heat of vaporization.
To transform a liquid into steam during the boiling process, a certain amount of heat must be transferred to it. The temperature of a liquid does not change when it boils. The transformation of a liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of the 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.
A quantity numerically equal to the amount of heat required to convert a liquid weighing 1 kg into steam at a constant temperature is called specific heat of vaporization.
The process of evaporation of a liquid occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of evaporation is equal to the specific heat of vaporization.
This value is denoted by the letter r and 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. For other liquids, for example 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 vapor, an amount of heat is required equal to:
Q p = rm. (13.6)
When steam condenses, the same amount of heat is released:
Q k = -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 between 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 to transform a crystalline substance weighing 1 kg at the melting point into a liquid is called specific heat of fusion and denoted by the letter λ.
When a substance weighing 1 kg crystallizes, exactly the same amount of heat is released as is absorbed during melting.
The specific heat of melting of ice is quite high: 3.34 10 5 J/kg.
“If ice did not have a high heat of fusion, then in the spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to the ice from the air. The consequences of this would be dire; after all, even in the current situation, large floods and strong flows of water arise when large masses of ice or snow melt.” R. Black, XVIII century.
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl = λm. (13.8)
The amount of heat released during crystallization of a body is equal to:
Q cr = -λm (13.9)
Heat balance equation.
Let us consider the heat exchange within a system consisting of several bodies that initially have different temperatures, for example, the heat exchange between water in a vessel and a hot iron ball lowered into the 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 amount of heat given is considered negative, the amount of heat received 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 are the amounts of heat received or given off by bodies. These amounts of heat are expressed by formula (13.5) or formulas (13.6)-(13.9), if various phase transformations of the substance (melting, crystallization, vaporization, condensation) occur during the heat exchange process.
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 by it 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 let's write down short condition (Given) and convert all quantities to the International System (SI).
|
Given: |
SI |
|
|
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 
.
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.
|
Required quantity |
Designation |
Units |
Basic formula |
Formula for quantity |
|
Quantity of heat |
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 amount of heat.
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: than more 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 the same initial temperature 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 amount of heat is denoted by the symbol Q. Like others different kinds energy, the amount 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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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 necessary 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 indicate the nutritional value of foods in 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- 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 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.