Calculation of heat. Quantity of heat
Heat capacity is the amount of heat absorbed by the body when heated by 1 degree.
The heat capacity of the body is indicated by a capital Latin letter FROM.
What determines the heat capacity of a body? First of all, from its mass. It is clear that heating, for example, 1 kilogram of water will require more heat than heating 200 grams.
What about the kind of substance? Let's do an experiment. Let's take two identical vessels and, pouring 400 g of water into one of them, and into the other - vegetable oil weighing 400 g, we will start heating them with the help of identical burners. By observing the readings of thermometers, we will see that the oil heats up quickly. To heat water and oil to the same temperature, the water must be heated longer. But the longer we heat the water, the large quantity heat it receives from the burner.
Thus, to heat the same mass of different substances to the same temperature, different amounts of heat are required. The amount of heat required to heat a body and, consequently, its heat capacity depend on the kind of substance of which this body is composed.
So, for example, to increase the temperature of 1 kg water by 1°C, an amount of heat equal to 4200 J is required, and to heat the same mass of sunflower oil by 1°C, an amount of heat equal to 1700 J is required.
Physical quantity, showing how much heat is required to heat 1 kg of a substance by 1 ºС, is called specific heat this substance.
Each substance has its own specific heat capacity, which is denoted by the Latin letter c and is measured in joules per kilogram-degree (J / (kg ° C)).
The specific heat capacity of the same substance in different aggregate states (solid, liquid and gaseous) is different. For example, the specific heat capacity of water is 4200 J/(kg ºС), and the specific heat capacity of ice is 2100 J/(kg ºС); aluminum in the solid state has a specific heat capacity of 920 J / (kg - ° C), and in the liquid state - 1080 J / (kg - ° C).
Note that water has a very high specific heat capacity. Therefore, the water in the seas and oceans, heating up in summer, absorbs from the air a large number of heat. Due to this, in those places that are located near large bodies of water, summer is not as hot as in places far from water.
Calculation of the amount of heat required to heat the body or released by it during cooling.
From the foregoing, it is clear that the amount of heat necessary to heat the body depends on the type of substance of which the body consists (i.e., its specific heat capacity) and on the mass of the body. It is also clear that the amount of heat depends on how many degrees we are going to increase the temperature of the body.
So, to determine the amount of heat required to heat the body or released by it during cooling, you need to multiply the specific heat of the body by its mass and the difference between its final and initial temperatures:
Q= cm (t 2 -t 1),
where Q- quantity of heat, c- specific heat capacity, m- body mass, t1- initial temperature, t2- final temperature.
When the body is heated t2> t1 and hence Q >0 . When the body is cooled t 2and< t1 and hence Q< 0 .
If the heat capacity of the whole body is known FROM, Q is determined by the formula: Q \u003d C (t 2 - t1).
22) Melting: definition, calculation of the amount of heat for melting or solidification, specific heat of melting, graph of t 0 (Q).
Thermodynamics
A branch of molecular physics that studies the transfer of energy, the patterns of transformation of some types of energy into others. In contrast to the molecular-kinetic theory, thermodynamics does not take into account internal structure substances and microparameters.
Thermodynamic system
This is a collection of bodies that exchange energy (in the form of work or heat) with each other or with environment. For example, the water in the teapot cools down, the exchange of heat of the water with the teapot and of the teapot with the environment takes place. Cylinder with gas under the piston: the piston performs work, as a result of which the gas receives energy and its macro parameters change.
Quantity of heat
it energy, which is received or given by the system in the process of heat exchange. Denoted by the symbol Q, measured, like any energy, in Joules.
As a result of various heat transfer processes, the energy that is transferred is determined in its own way.
Heating and cooling
This process is characterized by a change in the temperature of the system. The amount of heat is determined by the formula
The specific heat capacity of a substance with measured by the amount of heat required to heat up mass units of this substance by 1K. Heating 1 kg of glass or 1 kg of water requires a different amount of energy. Specific heat capacity is a known value already calculated for all substances, see the value in physical tables.
Heat capacity of substance C- this is the amount of heat that is necessary to heat the body without taking into account its mass by 1K.
Melting and crystallization
Melting is the transition of a substance from a solid to a liquid state. The reverse transition is called crystallization.
The energy spent on the destruction of the crystal lattice of a substance is determined by the formula
The specific heat of fusion is a known value for each substance, see the value in the physical tables.
Vaporization (evaporation or boiling) and condensation
Vaporization is the transition of a substance from a liquid (solid) state to a gaseous state. The reverse process is called condensation.
The specific heat of vaporization is a known value for each substance, see the value in the physical tables.
Combustion
The amount of heat released when a substance burns
The specific heat of combustion is a known value for each substance, see the value in the physical tables.
For a closed and adiabatically isolated system of bodies, the heat balance equation is satisfied. Algebraic sum the amount of heat given and received by all bodies participating in heat exchange is equal to zero:
Q 1 +Q 2 +...+Q n =0
23) The structure of liquids. surface layer. Surface tension force: examples of manifestation, calculation, surface tension coefficient.
From time to time, any molecule can move to an adjacent vacancy. Such jumps in liquids occur quite often; therefore, the molecules are not tied to certain centers, as in crystals, and can move throughout the entire volume of the liquid. This explains the fluidity of liquids. Due to the strong interaction between closely spaced molecules, they can form local (unstable) ordered groups containing several molecules. This phenomenon is called short-range order(Fig. 3.5.1).
The coefficient β is called temperature coefficient volume expansion . This coefficient for liquids is ten times greater than for solids. For water, for example, at a temperature of 20 ° C, β in ≈ 2 10 - 4 K - 1, for steel β st ≈ 3.6 10 - 5 K - 1, for quartz glass β kv ≈ 9 10 - 6 K - one .
The thermal expansion of water has an interesting and important anomaly for life on Earth. At temperatures below 4 °C, water expands with decreasing temperature (β< 0). Максимум плотности ρ в = 10 3 кг/м 3 вода имеет при температуре 4 °С.
When water freezes, it expands, so the ice remains floating on the surface of the freezing body of water. The temperature of freezing water under ice is 0°C. In denser layers of water near the bottom of the reservoir, the temperature is about 4 °C. Thanks to this, life can exist in the water of freezing reservoirs.
Most interesting feature liquids is the presence free surface . Liquid, unlike gases, does not fill the entire volume of the vessel into which it is poured. An interface is formed between liquid and gas (or vapor), which is in special conditions compared to the rest of the liquid mass. It should be borne in mind that, due to the extremely low compressibility, the presence of a more densely packed surface layer does not lead to any noticeable change in the liquid volume . If the molecule moves from the surface into the liquid, the forces of intermolecular interaction will do positive work. On the contrary, in order to pull a certain number of molecules from the depth of the liquid to the surface (i.e., increase the surface area of the liquid), external forces must do a positive work Δ A external, proportional to the change Δ S surface area:
It is known from mechanics that the equilibrium states of a system correspond to the minimum value of its potential energy. It follows that the free surface of the liquid tends to reduce its area. For this reason, a free drop of liquid takes on a spherical shape. The fluid behaves as if forces are acting tangentially to its surface, reducing (contracting) this surface. These forces are called surface tension forces .
The presence of surface tension forces makes the liquid surface look like an elastic stretched film, with the only difference that the elastic forces in the film depend on its surface area (i.e., on how the film is deformed), and the surface tension forces do not depend on the surface area of the liquid.
Some liquids, such as soapy water, have the ability to form thin films. All well-known soap bubbles have the correct spherical shape - this also manifests the action of surface tension forces. If a wire frame is lowered into the soapy solution, one of the sides of which is movable, then the whole of it will be covered with a film of liquid (Fig. 3.5.3).
Surface tension forces tend to shorten the surface of the film. To balance the moving side of the frame, an external force must be applied to it. If, under the action of the force, the crossbar moves by Δ x, then the work Δ A ext = F ext Δ x = Δ Ep = σΔ S, where ∆ S = 2LΔ x is the increment in the surface area of both sides of the soap film. Since the moduli of forces and are the same, we can write:
|
Thus, the surface tension coefficient σ can be defined as modulus of the surface tension force acting per unit length of the line bounding the surface.
Due to the action of surface tension forces in liquid droplets and inside soap bubbles overpressure occurs Δ p. If we mentally cut a spherical drop of radius R into two halves, then each of them must be in equilibrium under the action of surface tension forces applied to the boundary of the cut with a length of 2π R and overpressure forces acting on the area π R 2 sections (Fig. 3.5.4). The equilibrium condition is written as
If these forces are greater than the forces of interaction between the molecules of the liquid itself, then the liquid wets the surface of a solid body. In this case, the liquid approaches the surface of the solid body at some acute angle θ, which is characteristic of the given liquid-solid pair. The angle θ is called contact angle . If the interaction forces between liquid molecules exceed the forces of their interaction with solid molecules, then the contact angle θ turns out to be obtuse (Fig. 3.5.5). In this case, the liquid is said to does not wet the surface of a solid body. At complete wettingθ = 0, at complete non-wettingθ = 180°.
capillary phenomena called the rise or fall of fluid in small diameter tubes - capillaries. Wetting liquids rise through the capillaries, non-wetting liquids descend.
On fig. 3.5.6 shows a capillary tube of a certain radius r lowered by the lower end into a wetting liquid of density ρ. The upper end of the capillary is open. The rise of the liquid in the capillary continues until the force of gravity acting on the liquid column in the capillary becomes equal in absolute value to the resulting F n surface tension forces acting along the boundary of contact of the liquid with the surface of the capillary: F t = F n, where F t = mg = ρ hπ r 2 g, F n = σ2π r cos θ.
This implies:
With complete nonwetting, θ = 180°, cos θ = –1 and, therefore, h < 0. Уровень несмачивающей жидкости в капилляре опускается ниже уровня жидкости в сосуде, в которую опущен капилляр.
Water almost completely wets the clean glass surface. Conversely, mercury does not completely wet the glass surface. Therefore, the level of mercury in the glass capillary falls below the level in the vessel.
24) Vaporization: definition, types (evaporation, boiling), calculation of the amount of heat for vaporization and condensation, specific heat of vaporization.
Evaporation and condensation. Explanation of the phenomenon of evaporation based on ideas about the molecular structure of matter. Specific heat of vaporization. Her units.
The phenomenon of liquid turning into vapor is called vaporization.
Evaporation - the process of vaporization occurring from an open surface.
Molecules in a liquid move with different speeds. If any molecule is at the surface of the liquid, it can overcome the attraction of neighboring molecules and fly out of the liquid. The escaping molecules form vapor. The velocities of the remaining liquid molecules change upon collision. In this case, some molecules acquire a speed sufficient to fly out of the liquid. This process continues, so liquids evaporate slowly.
*Evaporation rate depends on the type of liquid. Those liquids evaporate faster, in which the molecules are attracted with less force.
*Evaporation can occur at any temperature. But at higher temperatures, evaporation is faster .
*Evaporation rate depends on its surface area.
*With wind (air flow), evaporation occurs faster.
During evaporation, the internal energy decreases, because. during evaporation, fast molecules leave the liquid, therefore, the average speed of the remaining molecules decreases. This means that if there is no influx of energy from outside, then the temperature of the liquid decreases.
The phenomenon of the transformation of vapor into liquid is called condensation.
It is accompanied by the release of energy.
Vapor condensation explains the formation of clouds. Water vapor rising above the ground forms clouds in the upper cold layers of air, which consist of tiny drops of water.
Specific heat of vaporization - physical. a quantity indicating how much heat is required to turn a liquid of mass 1 kg into vapor without changing the temperature.
Oud. heat of vaporization denoted by the letter L and is measured in J / kg
Oud. heat of vaporization of water: L=2.3×10 6 J/kg, alcohol L=0.9×10 6
The amount of heat required to turn a liquid into steam: Q = Lm
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 transfer, a change in the internal energy of the body occurs. 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).
« Physics - Grade 10 "
In what processes does aggregate transformation of matter occur?
How can the state of matter be changed?
You can change the internal energy of any body by doing work, heating or, conversely, cooling it.
Thus, when forging a metal, work is done and it is heated, while 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 hence 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, slowly moving molecules of a cold body interact with rapidly moving molecules of a hot body. As a result, the kinetic energies of the molecules are equalized and the velocities of the molecules of a cold body increase, while those of a hot body decrease.
During heat exchange, there is no conversion of energy from one form to another; part of the internal energy of a hotter body is transferred to a less heated body.
The amount of heat and heat capacity.
You already know that in order to heat a body with mass m from temperature t 1 to temperature t 2, it is necessary to transfer to it the amount of heat:
Q \u003d cm (t 2 - t 1) \u003d cm Δt. (13.5)
When the 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 value numerically equal to the amount of heat that a substance with a mass of 1 kg receives or gives off when its temperature changes by 1 K.
The specific heat capacity of gases depends on the process by which heat is transferred. 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.
Liquids and solids expand slightly when heated. Their specific heat capacities at constant volume and constant pressure differ little.
Specific heat of vaporization.
To convert a liquid into vapor during the boiling process, it is necessary to transfer a certain amount of heat to it. The temperature of a liquid does not change when it boils. The transformation of liquid into vapor at a constant temperature does not lead to an increase in the kinetic energy of 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.
The value numerically equal to the amount of heat required to convert a 1 kg liquid into steam at a constant temperature is called specific heat vaporization.
The process of liquid evaporation occurs at any temperature, while the fastest molecules leave the liquid, and it cools during evaporation. The specific heat of vaporization is equal to the specific heat of vaporization.
This value is denoted by the letter r and is 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. In other liquids, such as 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 steam, an amount of heat is required equal to:
Q p \u003d rm. (13.6)
When steam condenses, the same amount of heat is released:
Q k \u003d -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 of molecules. The kinetic energy of the molecules does not change, since melting occurs at a constant temperature.
The value numerically equal to the amount of heat required to transform a crystalline substance weighing 1 kg at a melting point into a liquid is called specific heat of fusion and are denoted by the letter λ.
During the crystallization of a substance with a mass of 1 kg, exactly the same amount of heat is released as is absorbed during melting.
The specific heat of melting of ice is rather high: 3.34 10 5 J/kg.
“If ice did not have a high heat of fusion, then in spring the entire mass of ice would have to melt in a few minutes or seconds, since heat is continuously transferred to ice from the air. The consequences of this would be dire; for even under the present situation great floods and great torrents of water arise from the melting of great masses of ice or snow.” R. Black, 18th century
In order to melt a crystalline body of mass m, an amount of heat is required equal to:
Qpl \u003d λm. (13.8)
The amount of heat released during the crystallization of the body is equal to:
Q cr = -λm (13.9)
Heat balance equation.
Consider heat transfer within a system consisting of several bodies with initially various temperatures, for example, heat exchange between water in a vessel and a hot iron ball lowered into 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 given amount of heat is considered negative, the received amount of heat 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 - the amount of heat received or given away by the bodies. These quantities of heat are expressed by formula (13.5) or formulas (13.6) - (13.9), if various phase transformations of the substance occur in the process of heat transfer (melting, crystallization, vaporization, condensation).
HEAT EXCHANGE.
1.Heat transfer.
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 is the heat exchange between bodies in direct contact.
2) Convection is heat transfer in which heat is transferred by gas or liquid flows.
3) Radiation is heat transfer by means of electromagnetic radiation.
2. The 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 letter Q.
The unit of measurement of the amount of heat = 1 J.
The amount of heat received by a body from another body as a result of heat transfer can be spent on increasing the temperature (increasing the kinetic energy of molecules) or on changing the state of aggregation (increasing potential energy).
3. Specific heat capacity of a 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 body mass m and the temperature difference (T 2 - T 1), i.e.
Q = cm(T 2 - T 1 ) = withmΔ 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 in order to heat it by 1 K.
Unit of specific heat capacity =.
The heat capacity values of 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 vapor is proportional to the mass of the liquid, i.e.
Q = lm,
where is the coefficient of proportionality L is called the specific heat of vaporization.
The specific heat of vaporization is equal to the amount of heat that is necessary to convert 1 kg of liquid at the boiling point into steam.
Unit of measure for the specific heat of vaporization.
In the reverse process, the condensation of steam, heat is released in the same amount that was spent on vaporization.
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 coefficient of proportionality λ is called the specific heat of fusion.
The specific heat of fusion is equal to the amount of heat that is necessary to turn a solid body weighing 1 kg into a liquid at the melting point.
Unit of measure for specific heat of fusion.
In the reverse process, the crystallization of a 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 the complete combustion of the fuel is proportional to the mass of the fuel, i.e.
Q = qm,
Where the proportionality factor q is called the specific heat of combustion.
The specific heat of combustion is equal to the amount of heat that is released during the complete combustion of 1 kg of fuel.
Unit of measure for specific heat of combustion.
7. Heat balance equation.
Two or more bodies are involved in heat exchange. Some bodies give off heat, while others receive it. Heat transfer occurs until the temperatures of the bodies become equal. According to the law of conservation of energy, the amount of heat that is given off is equal to the amount that is received. On this basis, the heat balance equation is written.
Consider an example.
A body of mass m 1 , whose heat capacity is c 1 , has temperature T 1 , and a body of mass m 2 , whose heat capacity is c 2 , has 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 a hot body is transferred to a cold one, and the temperatures even out. Let us denote the final total 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 us open the brackets and express the value of the total steady-state temperature θ.
The temperature value θ in this case will be obtained in kelvins.
However, since in the expressions for Q passed. and Q is received. if there is a difference between two temperatures, and it is the same in both kelvins and degrees Celsius, then the calculation can be carried out in degrees Celsius. Then
In this case, the temperature value θ will be obtained in degrees Celsius.
The alignment of temperatures as a result of heat conduction can be explained on the basis of molecular kinetic theory as the exchange of kinetic energy between molecules during collision in the process of thermal chaotic motion.
This example can be illustrated with a graph. 
