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).
|
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 |
In this lesson we will continue to study the internal energy of the body, and more specifically, ways to change it. And the subject of our attention this time will be heat transfer. We will remember what types it is divided into, what it is measured in, and by what ratios we can calculate the amount of heat transferred as a result of heat exchange; we will also give a definition of the specific heat capacity of a body.
Topic: Fundamentals of thermodynamics
Lesson: Amount of heat. Specific heat
As we already know from elementary school, and as we recalled in the last lesson, there are two ways to change the internal energy of a body: doing work on it or transferring a certain amount of heat to it. We already know about the first method from, again, the last lesson, but we also talked a lot about the second in the eighth grade course.
The process of transferring heat (amount of heat or energy) without doing work is called heat exchange or heat transfer. According to transmission mechanisms, as we know, it is divided into three types:
- Thermal conductivity
- Convection
- Radiation
As a result of one of these processes, a certain amount of heat is transferred to the body, the value of which, in fact, changes the internal energy. Let us characterize this quantity.
Definition. Quantity of heat. Designation - Q. Units of measurement - J. When body temperature changes (which is equivalent to a change in internal energy), the amount of heat expended on this change can be calculated using the formula:
Here: - body weight; - specific heat capacity of the body; - change in body temperature.
Moreover, if, that is, during cooling, they say that the body gave up a certain amount of heat, or a negative amount of heat was transferred to the body. If, that is, heating of the body is observed, the amount of heat transferred, of course, will be positive.
Special attention should be paid to the specific heat capacity of the body.
Definition. Specific heat- a value numerically equal to the amount of heat that must be transferred to heat one kilogram of a substance by one degree. Specific heat capacity is an individual value for each individual substance. Therefore, this is a tabular value, obviously known, provided that we know which portion of the substance heat is transferred to.
The SI unit of specific heat can be obtained from the above equation:
Thus:
Let us now consider cases when the transfer of a certain amount of heat leads to a change in the state of aggregation of a substance. Let us recall that such transitions are called melting, crystallization, evaporation and condensation.
When moving from a liquid to a solid and vice versa, the amount of heat is calculated using the formula:
Here: - body weight; - specific heat melting of a body (the amount of heat required to completely melt one kilogram of a substance).
In order to melt a body, it needs to transfer a certain amount of heat, and during condensation the body itself releases environment a certain amount of heat.
When moving from a liquid to a gaseous body and vice versa, the amount of heat is calculated by the formula:
Here: - body weight; - specific heat of vaporization of a body (the amount of heat required to completely evaporate one kilogram of a substance).
In order to evaporate a liquid, it needs to transfer a certain amount of heat, and when condensing, the vapor itself releases a certain amount of heat into the environment.
It should also be emphasized that both melting with crystallization and evaporation with condensation take place at a constant temperature (melting and boiling points, respectively) (Fig. 1).
Rice. 1. Graph of the dependence of temperature (in degrees Celsius) on the amount of substance received ()
Separately, it is worth noting the calculation of the amount of heat released during the combustion of a certain mass of fuel:
Here: - mass of fuel; - specific heat of combustion of fuel (the amount of heat released during the combustion of one kilogram of fuel).
Particular attention should be paid to the fact that, in addition to the fact that different substances specific heat capacities are taken different meanings, this parameter can be different for the same substance at different conditions. For example, different values of specific heat capacities are distinguished for heating processes occurring at constant volume () and for processes occurring at constant pressure ().
There is also a distinction between molar heat capacity and simply heat capacity.
Definition. Molar heat capacity () - the amount of heat required to heat one mole of a substance by one degree.
Heat capacity (C) - the amount of heat required to heat a portion of a substance of a certain mass by one degree. Relationship between heat capacity and specific heat capacity:
In the next lesson, we will look at such an important law as the first law of thermodynamics, which relates the change in internal energy to the work of the gas and the amount of heat transferred.
Bibliography
- Myakishev G.Ya., Sinyakov A.Z. Molecular physics. Thermodynamics. - M.: Bustard, 2010.
- Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Ilexa, 2005.
- Kasyanov V.A. Physics 10th grade. - M.: Bustard, 2010.
- Dictionaries and encyclopedias on Academician ().
- Tt.pstu.ru ().
- Elementy.ru ().
Homework
- Page 83: No. 643-646. Physics. Problem book. 10-11 grades. Rymkevich A.P. - M.: Bustard, 2013. ()
- How are molar and specific heat capacities related?
- Why do window surfaces sometimes fog up? Which side of the windows does this happen on?
- In what weather do puddles dry out faster: calm or windy?
- *What is the heat received by the body during melting spent on?
« 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 a cold body increase, and those of a 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 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 for the transformation 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 when melting occur large masses ice or snow." R. Black, XVIII century.
To melt crystalline body mass m, the required amount of heat is 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.
As is known, during various mechanical processes a change in mechanical energy occurs W meh. A measure of the change in mechanical energy is the work of forces applied to the system:
\(~\Delta W_(meh) = A.\)
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 mass m on temperature T 1 to temperature T 2, calculated by the formula
\(~Q = cm (T_2 - T_1) = cm \Delta T, \qquad (1)\)
Where c- specific heat capacity of the substance;
\(~c = \frac(Q)(m (T_2 - T_1)).\)
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 C T is numerically equal to the amount of heat required to change body temperature by 1 K:
\(~C_T = \frac(Q)(T_2 - T_1) = cm.\)
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
\(~Q = Lm, \qquad (2)\)
Where L- specific heat of vaporization. When steam condenses, the same amount of heat is released.
In order to melt a crystalline body weighing m at the melting point, the body needs to communicate the amount of heat
\(~Q = \lambda m, \qquad (3)\)
Where λ - specific heat of fusion. When a body crystallizes, the same amount of heat is released.
The amount of heat released during complete combustion of a mass of fuel m,
\(~Q = qm, \qquad (4)\)
Where q- specific heat of combustion.
The SI unit of specific heats of vaporization, melting and combustion is joule per kilogram (J/kg).
Literature
Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyhavanne, 2004. - P. 154-155.