Marry 

The unit of measure for the amount of heat. Quantity of heat. Heat balance equation

The process of transferring energy from one body to another without doing work is called heat exchange or heat transfer. Heat transfer occurs between bodies that have different temperatures. When contact is established between bodies with different temperatures, a part of the internal energy is transferred from a body with a higher temperature to a body with a lower temperature. The energy transferred to the body as a result of heat transfer is called amount of heat.

Specific heat capacity of a substance:

If the heat transfer process is not accompanied by work, then, based on the first law of thermodynamics, the amount of heat is equal to the change in the internal energy of the body: .

The average energy of the random translational motion of molecules is proportional to the absolute temperature. The change in the internal energy of a body is equal to the algebraic sum of the changes in the energy of all atoms or molecules, the number of which is proportional to the mass of the body, so the change in internal energy and, consequently, the amount of heat is proportional to the mass and temperature change:


The proportionality factor in this equation is called specific heat capacity of a substance. The specific heat capacity indicates how much heat is needed to raise the temperature of 1 kg of a substance by 1 K.

Work in thermodynamics:

In mechanics, work is defined as the product of the modules of force and displacement and the cosine of the angle between them. Work is done when a force acts on a moving body and is equal to the change in its kinetic energy.

In thermodynamics, the motion of a body as a whole is not considered; we are talking about the movement of parts of a macroscopic body relative to each other. As a result, the volume of the body changes, and its velocity remains equal to zero. Work in thermodynamics is defined in the same way as in mechanics, but it is equal to the change not in the kinetic energy of the body, but in its internal energy.

When work is done (compression or expansion), the internal energy of the gas changes. The reason for this is as follows: during elastic collisions of gas molecules with a moving piston, their kinetic energy changes.

Let us calculate the work of the gas during expansion. The gas acts on the piston with a force
, where is the pressure of the gas, and - surface area piston. As the gas expands, the piston moves in the direction of the force for a short distance
. If the distance is small, then the gas pressure can be considered constant. The work of the gas is:

Where
- change in gas volume.

In the process of expanding the gas, it does positive work, since the direction of force and displacement coincide. In the process of expansion, the gas gives off energy to the surrounding bodies.

The work done by external bodies on a gas differs from the work of a gas only in sign
, because the strength acting on the gas is opposite to the force , with which the gas acts on the piston, and is equal to it in absolute value (Newton's third law); and the movement remains the same. Therefore, the work of external forces is equal to:

.

First law of thermodynamics:

The first law of thermodynamics is the law of conservation of energy, extended to thermal phenomena. Law of energy conservation: energy in nature does not arise from nothing and does not disappear: the amount of energy is unchanged, it only changes from one form to another.

In thermodynamics, bodies are considered, the position of the center of gravity of which practically does not change. The mechanical energy of such bodies remains constant, and only the internal energy can change.

Internal energy can be changed in two ways: heat transfer and work. In the general case, the internal energy changes both due to heat transfer and due to the performance of work. The first law of thermodynamics is formulated precisely for such general cases:

The change in the internal energy of the system during its transition from one state to another is equal to the sum of the work of external forces and the amount of heat transferred to the system:

If the system is isolated, then no work is done on it and it does not exchange heat with the surrounding bodies. According to the first law of thermodynamics the internal energy of an isolated system remains unchanged.

Given that
, the first law of thermodynamics can be written as follows:

The amount of heat transferred to the system goes to change its internal energy and to perform work on external bodies by the system.

Second law of thermodynamics: it is impossible to transfer heat from a colder system to a hotter one in the absence of other simultaneous changes in both systems or in the surrounding bodies.

The change in internal energy by doing work is characterized by the amount of work, i.e. work is a measure of the change in internal energy in a given process. The change in the internal energy of a body during heat transfer is characterized by a quantity called the amount of heat.

is the change in the internal energy of the body in the process of heat transfer without doing work. The amount of heat is denoted by the letter Q .

Work, internal energy and the amount of heat are measured in the same units - joules ( J), like any other form of energy.

In thermal measurements, a special unit of energy, the calorie ( feces), equal to the amount of heat required to raise the temperature of 1 gram of water by 1 degree Celsius (more precisely, from 19.5 to 20.5 ° C). This unit, in particular, is currently used in calculating the consumption of heat (thermal energy) in apartment buildings. Empirically, the mechanical equivalent of heat has been established - the ratio between calories and joules: 1 cal = 4.2 J.

When a body transfers a certain amount of heat without doing work, its internal energy increases, if a body gives off a certain amount of heat, then its internal energy decreases.

If you pour 100 g of water into two identical vessels, and 400 g into another at the same temperature and put them on the same burners, then the water in the first vessel will boil earlier. Thus, the greater the mass of the body, the greater the amount of heat it needs to heat up. The same goes for cooling.

The amount of heat required to heat a body also depends on the kind of substance from which this body is made. This dependence of the amount of heat required to heat the body on the type of substance is characterized by a physical quantity called specific heat capacity substances.

- this is a physical quantity equal to the amount of heat that must be reported to 1 kg of a substance to heat it by 1 ° C (or 1 K). The same amount of heat is given off by 1 kg of a substance when cooled by 1 °C.

The specific heat capacity is denoted by the letter with. The unit of specific heat capacity is 1 J/kg °C or 1 J/kg °K.

The values ​​of the specific heat capacity of substances are determined experimentally. Liquids have a higher specific heat capacity than metals; Water has the highest specific heat capacity, gold has a very small specific heat capacity.

Since the amount of heat is equal to the change in the internal energy of the body, we can say that the specific heat capacity shows how much the internal energy changes 1 kg substance when its temperature changes 1 °C. In particular, the internal energy of 1 kg of lead, when it is heated by 1 °C, increases by 140 J, and when it is cooled, it decreases by 140 J.

Q required to heat the body mass m temperature t 1 °С up to temperature t 2 °С, is equal to the product of the specific heat capacity of the substance, body mass and the difference between the final and initial temperatures, i.e.

Q \u003d c ∙ m (t 2 - t 1)

According to the same formula, the amount of heat that the body gives off when cooled is also calculated. Only in this case should the final temperature be subtracted from the initial temperature, i.e. Subtract the smaller temperature from the larger temperature.

This is a synopsis on the topic. "Quantity of heat. Specific heat". Choose next steps:

  • Go to the next abstract:

The focus of our article is the amount of heat. We will consider the concept of internal energy, which is transformed when this value changes. We will also show some examples of the application of calculations in human activity.

Heat

With any word of the native language, each person has his own associations. They are determined by personal experience and irrational feelings. What is usually represented by the word "warmth"? A soft blanket, a working central heating battery in winter, the first sunlight in spring, a cat. Or a mother's look, a comforting word from a friend, timely attention.

Physicists mean by this a very specific term. And very important, especially in some sections of this complex but fascinating science.

Thermodynamics

It is not worth considering the amount of heat in isolation from the simplest processes on which the law of conservation of energy is based - nothing will be clear. Therefore, to begin with, we remind our readers.

Thermodynamics considers any thing or object as a combination of a very large number of elementary parts - atoms, ions, molecules. Its equations describe any change in the collective state of the system as a whole and as part of the whole when changing macro parameters. The latter are understood as temperature (denoted as T), pressure (P), concentration of components (usually C).

Internal energy

Internal energy is a rather complicated term, the meaning of which should be understood before talking about the amount of heat. It denotes the energy that changes with an increase or decrease in the value of the object's macro parameters and does not depend on the reference system. It is part of the total energy. It coincides with it under conditions when the center of mass of the thing under study is at rest (that is, there is no kinetic component).

When a person feels that some object (say, a bicycle) has warmed up or cooled down, this shows that all the molecules and atoms that make up this system have experienced a change in internal energy. However, the constancy of temperature does not mean the preservation of this indicator.

Work and warmth

The internal energy of any thermodynamic system can be transformed in two ways:

  • by doing work on it;
  • during heat exchange with the environment.

The formula for this process looks like this:

dU=Q-A, where U is internal energy, Q is heat, A is work.

Let the reader not be deceived by the simplicity of the expression. The permutation shows that Q=dU+A, but the introduction of entropy (S) brings the formula to the form dQ=dSxT.

Since in this case the equation takes the form of a differential equation, the first expression requires the same. Further, depending on the forces acting in the object under study and the parameter that is being calculated, the necessary ratio is derived.

Let us take a metal ball as an example of a thermodynamic system. If you put pressure on it, throw it up, drop it into a deep well, then this means doing work on it. Outwardly, all these harmless actions will not cause any harm to the ball, but its internal energy will change, albeit very slightly.

The second way is heat transfer. Now we come to the main goal of this article: a description of what the amount of heat is. This is such a change in the internal energy of a thermodynamic system that occurs during heat transfer (see the formula above). It is measured in joules or calories. Obviously, if the ball is held over a lighter, in the sun, or simply in a warm hand, it will heat up. And then, by changing the temperature, you can find the amount of heat that was communicated to him at the same time.

Why gas is the best example of a change in internal energy, and why students don't like physics because of it

Above, we described changes in the thermodynamic parameters of a metal ball. They are not very noticeable without special devices, and the reader is left to take a word about the processes occurring with the object. Another thing is if the system is gas. Press on it - it will be visible, heat it up - the pressure will rise, lower it underground - and this can be easily fixed. Therefore, in textbooks, it is gas that is most often taken as a visual thermodynamic system.

But, alas, not much attention is paid to real experiments in modern education. A scientist who writes a methodological manual understands perfectly well what is at stake. It seems to him that, using the example of gas molecules, all thermodynamic parameters will be adequately demonstrated. But for a student who is just discovering this world, it is boring to hear about an ideal flask with a theoretical piston. If the school had real research laboratories and dedicated hours to work in them, everything would be different. So far, unfortunately, the experiments are only on paper. And, most likely, this is precisely what causes people to consider this branch of physics as something purely theoretical, far from life and unnecessary.

Therefore, we decided to give the bicycle already mentioned above as an example. A person presses on the pedals - does work on them. In addition to communicating torque to the entire mechanism (due to which the bicycle moves in space), the internal energy of the materials from which the levers are made changes. The cyclist pushes the handles to turn, and again does the work.

The internal energy of the outer coating (plastic or metal) is increased. A person goes to a clearing under the bright sun - the bike heats up, its amount of heat changes. Stops to rest in the shade of an old oak tree and the system cools down, wasting calories or joules. Increases speed - increases the exchange of energy. However, the calculation of the amount of heat in all these cases will show a very small, imperceptible value. Therefore, it seems that there are no manifestations of thermodynamic physics in real life.

Application of calculations for changes in the amount of heat

Probably, the reader will say that all this is very informative, but why are we so tortured at school with these formulas. And now we will give examples in which areas of human activity they are directly needed and how this applies to anyone in his everyday life.

To begin with, look around you and count: how many metal objects surround you? Probably more than ten. But before becoming a paper clip, wagon, ring or flash drive, any metal is smelted. Every plant that processes, say, iron ore must understand how much fuel is required in order to optimize costs. And when calculating this, it is necessary to know the heat capacity of the metal-containing raw materials and the amount of heat that must be imparted to it in order for all technological processes to take place. Since the energy released by a unit of fuel is calculated in joules or calories, the formulas are needed directly.

Or another example: most supermarkets have a department with frozen goods - fish, meat, fruits. Where raw materials from animal meat or seafood are turned into a semi-finished product, they must know how much electricity refrigeration and freezing units will use per ton or unit of the finished product. To do this, you should calculate how much heat a kilogram of strawberries or squids loses when cooled by one degree Celsius. And in the end, this will show how much electricity a freezer of a certain capacity will spend.

Planes, ships, trains

Above, we have shown examples of relatively immobile, static objects that are informed or, on the contrary, a certain amount of heat is taken away from them. For objects moving in the process of operation in conditions of constantly changing temperature, calculations of the amount of heat are important for another reason.

There is such a thing as "metal fatigue". It also includes the maximum allowable loads at a certain rate of temperature change. Imagine an airplane taking off from the humid tropics into the frozen upper atmosphere. Engineers have to work hard so that it does not fall apart due to cracks in the metal that appear when the temperature changes. They are looking for an alloy composition that can withstand real loads and will have a large margin of safety. And in order not to search blindly, hoping to accidentally stumble upon the desired composition, you have to do a lot of calculations, including those that include changes in the amount of heat.

Definition

The amount of heat or simply warmth($Q$) is called the internal energy, which, without doing work, is transferred from bodies with a higher temperature to bodies with a lower temperature in the processes of heat conduction or radiation.

Joule - SI unit for measuring the amount of heat

The unit of heat quantity can be obtained from the first law of thermodynamics:

\[\Delta Q=A+\Delta U\ \left(1\right),\]

where $A$ is the work of the thermodynamic system; $\Delta U$ - change in internal energy of the system; $\Delta Q$ - the amount of heat supplied to the system.

From law (1), and even more so from its version for an isothermal process:

\[\Delta Q=A\ \left(2\right).\]

Obviously, in the International System of Units (SI), the joule (J) is a unit of energy and work.

It is easy to express the joule in basic units using the definition of energy ($E$) of the form:

where $c$ is the speed of light; $m$ - body weight. Based on expression (2), we have:

\[\left=\left=kg\cdot (\left(\frac(m)(s)\right))^2=\frac(kg\cdot m^2)(s^2).\]

With the joule, all standard prefixes of the SI system are used, denoting decimal fractional and multiple units. For example, $1kJ=(10)^3J$; 1MJ = $(10)^6J$; 1 GJ=$(10)^9J$.

Erg - unit of measurement of the amount of heat in the cgs system

In the CGS system (centimeter, gram, second), heat is measured in ergs (ergs). In this case, one erg is equal to:

Taking into account that:

we get the ratio between joule and erg:

Calorie - a unit of measure for the amount of heat

The calorie is used as an off-system unit for measuring the amount of heat. One calorie is equal to the amount of heat that must be transferred to water weighing one kilogram in order to heat it by one degree Celsius. The relationship between joule and calorie is as follows:

To be more precise, they distinguish:

  • International calorie, it is equal to:
    • \
  • thermochemical calorie:
    • \
  • 15 degree calorie used for thermal measurements:
    • \

Calories are often used with decimal prefixes such as: kcal (kilocalorie) $1kcal=(10)^3cal$; Mcal (megacalorie) 1Mcal = $(10)^6cal$; Gcal (gigacalorie) 1 Gcal=$(10)^9cal$.

Sometimes a kilocalorie is called a big calorie or kilogram-calorie.

Examples of problems with a solution

Example 1

Exercise. How much heat is absorbed by hydrogen of mass $m=0.2$kg when it is heated from $t_1=0(\rm()^\circ\!C)$ to $t_2=100(\rm()^\circ\! C)$ at constant pressure? Write your answer in kilojoules.

Decision. We write the first law of thermodynamics:

\[\Delta Q=A+\Delta U\ \left(1.1\right).\]

\[\Delta U=\frac(i)(2)\frac(m)(\mu )R\Delta T\ \left(1.2\right),\]

where $i=5$ is the number of degrees of freedom of the hydrogen molecule; $\mu =2\cdot (10)^(-3)\frac(kg)(mol)$; $R=8.31\ \frac(J)(mol\cdot K)$; $\Delta T=t_2-t_1$. By assumption, we are dealing with an isobaric process. Work in an isobaric process is equal to:

Taking into account expressions (1.2) and (1.3), we transform the first law of thermodynamics for the isobaric process to the form:

\[\Delta Q=\frac(m)(\mu )R\Delta T\ +\frac(i)(2)\frac(m)(\mu )R\Delta T=\frac(m)(\ mu )R\Delta T\left(1+\frac(i)(2)\right)\ \left(1.4\right).\]

Let's check in what units the heat is measured, if it is calculated by the formula (1.4):

\[\left[\Delta Q\right]=\left[\frac(m)(\mu )R\Delta T\left(1+\frac(i)(2)\right)\right]=\left [\frac(m)(\mu )R\Delta T\right]=\frac(\left)(\left[\mu \right])\left\left[\Delta T\right]=\frac(kg )(kg/mol)\cdot \frac(J)(mol\cdot K)\cdot K=J.\]

Let's do the calculations:

\[\Delta Q=\frac(0,2)(2 (10)^(-3))\cdot 8,31\cdot 100\left(1+\frac(5)(2)\right)\approx 291\cdot (10)^3\left(J\right)=291\ \left(kJ\right).\]

Answer.$\Delta Q=291\ $ kJ

Example 2

Exercise. Helium having a mass $m=1\r$ was heated by 100 K in the process shown in Fig.1. How much heat is transferred to the gas? Write your answer in CGS units.

Decision. Figure 1 depicts an isochoric process. For such a process, we write the first law of thermodynamics as:

\[\Delta Q=\Delta U\ \left(2.1\right).\]

We find the change in internal energy as:

\[\Delta U=\frac(i)(2)\frac(m)(\mu )R\Delta T\ \left(2.2\right),\]

where $i=3$ is the number of degrees of freedom of a helium molecule; $\mu =4\frac(g)(mol)$; $R=8.31\cdot (10)^7\ \frac(erg)(mol\cdot K)$; $\Delta T=100\ K.$ All values ​​are written in CGS. Let's do the calculations:

\[\Delta Q=\frac(3)(2)\cdot \frac(1)(4)\cdot 8,31\cdot (10)^7\cdot 100\approx 3\cdot (10)^9( erg)\ \]

Answer.$\Delta Q=3\cdot (10)^9$ erg

“...- How many parrots will fit in you, such is your height.
- Really needed! I will not swallow so many parrots! ... "

From m / f "38 parrots"

In accordance with international SI (International System of Units) rules, the amount of thermal energy or the amount of heat is measured in Joules [J], there are also multiple units of kiloJoule [kJ] = 1000 J., MegaJoule [MJ] = 1,000,000 J, GigaJoule [ GJ] = 1,000,000,000 J., etc. This unit of measurement of thermal energy is the main international unit and is most often used in scientific and scientific and technical calculations.

However, all of us know or at least once heard another unit for measuring the amount of heat (or just heat) is a calorie, as well as a kilocalorie, Megacalorie and Gigacalorie, which means the prefixes kilo, Giga and Mega, see the example with Joules above. In our country, it has historically developed so that when calculating tariffs for heating, whether it is heating with electricity, gas or pellet boilers, it is customary to consider the cost of exactly one Gigacalorie of thermal energy.

So what is Gigacalorie, kilowatt, kilowatt * hour or kilowatt / hour and Joules and how are they related?, you will learn in this article.

So, the basic unit of thermal energy is, as already mentioned, the Joule. But before talking about units of measurement, it is necessary, in principle, to explain at the household level what thermal energy is and how and why to measure it.

We all know from childhood that in order to get warm (to get thermal energy) you need to set something on fire, so we all lit fires, the traditional fuel for a fire is firewood. Thus, obviously, during the combustion of fuel (any: firewood, coal, pellets, natural gas, diesel fuel), thermal energy (heat) is released. But in order to heat, for example, different volumes of water, a different amount of firewood (or other fuel) is required. It is clear that a few fires in a fire are enough to heat two liters of water, and to cook half a bucket of soup for the whole camp, you need to stock up on several bundles of firewood. In order not to measure such strict technical quantities as the amount of heat and the heat of combustion of fuel with bundles of firewood and buckets of soup, heat engineers decided to bring clarity and order and agreed to invent a unit for the amount of heat. For this unit to be the same everywhere, it was defined as follows: it takes 4,190 calories, or 4.19 kilocalories, to heat one kilogram of water by one degree under normal conditions (atmospheric pressure), therefore, to heat one gram of water, a thousand times less heat will be enough - 4.19 calories.

The calorie is related to the international unit of thermal energy, the Joule, as follows:

1 calorie = 4.19 Joules.

Thus, it takes 4.19 Joules of thermal energy to heat 1 gram of water by one degree, and 4,190 Joules of heat to heat one kilogram of water.

In technology, along with the unit of measurement of thermal (and any other) energy, there is a unit of power and, in accordance with the international system (SI), this is Watt. The concept of power is also applicable to heating devices. If a heating device is capable of delivering 1 Joule of thermal energy in 1 second, then its power is 1 watt. Power is the ability of a device to produce (create) a certain amount of energy (in our case, thermal energy) per unit of time. Returning to our example with water, to heat one kilogram (or one liter, in the case of water, a kilogram is equal to a liter) of water by one degree Celsius (or Kelvin, whatever), we need a power of 1 kilocalorie or 4,190 J. of thermal energy. To heat one kilogram of water in 1 second of time by 1 degree, we need a device of the following power:

4190 J./1 s. = 4 190 W. or 4.19 kW.

If we want to heat our kilogram of water by 25 degrees in the same second, then we need twenty-five times more power, i.e.

4.19 * 25 \u003d 104.75 kW.

Thus, we can conclude that the power of 104.75 kW. heats 1 liter of water by 25 degrees in one second.

Since we got to Watts and kilowatts, we should also put in a word about them. As already mentioned, a watt is a unit of power, including the thermal power of the boiler, but in addition to gas boilers, electric boilers are also familiar to mankind, the power of which is measured, of course, in the same kilowatts and they consume not pellets or gas, but electricity , which is measured in kilowatt hours. The correct spelling of the unit of energy is kilowatt * hour (namely, kilowatt multiplied by an hour, not divided), writing kW / hour is a mistake!

In electric boilers, electrical energy is converted into thermal energy (the so-called Joule heat), and if the boiler consumed 1 kWh of electricity, how much heat did it generate? To answer this simple question, you need to perform a simple calculation.

Converting kilowatts to kilojoules/seconds (kilojoules per second) and hours to seconds: there are 3,600 seconds in one hour, we get:

1 kW*h =[ 1 kJ/s]*3600 s.=1,000 J *3600 s = 3,600,000 Joules or 3.6 MJ.

So,

1 kWh = 3.6 MJ.

In turn, 3.6 MJ / 4.19 \u003d 0.859 Mcal \u003d 859 kcal \u003d 859,000 cal. Energy (thermal).

Now let's move on to Gigacalorie, the price of which for various types of fuel like to be considered by heat engineers.

1 Gcal = 1,000,000,000 cal.

1,000,000,000 cal. \u003d 4.19 * 1,000,000,000 \u003d 4,190,000,000 J. \u003d 4,190 MJ. = 4.19 GJ.

Or, knowing that 1 kWh = 3.6 MJ, we recalculate 1 Gigacalorie per kilowatt*hour:

1 Gcal = 4190 MJ/3.6 MJ = 1163 kWh!

If, after reading this article, you decide to consult with a specialist of our company on any issue related to heat supply, then you