Thermophysics. Теплофизика

№ 3560 министерство науки И высшего образования рф
ФЕДЕРАЛЬНОЕ ГОСУДАРСТВЕННОЕ АВТОНОМНОЕ ОБРАЗОВАТЕЛЬНОЕ УЧРЕЖДЕНИЕ ВЫСШЕГО ОБРАЗОВАНИЯ
«НАЦИОНАЛЬНЫЙ ИССЛЕДОВАТЕЛЬСКИЙ ТЕХНОЛОГИЧЕСКИЙ УНИВЕРСИТЕТ «МИСиС»

ИНСТИТУТ ЭКОТЕХНОЛОГИЙ И ИНЖИНИРИНГА
Кафедра энергоэффективных и ресурсосберегающих промышленных технологий
И.А. Прибытков





        THERMOPHYSICS (ТЕПЛОФИЗИКА)

Учебное пособие


Рекомендовано редакционно-издательским советом университета







        МИСиС


Москва 2019

УДК 669.04
     П75

Рецензенты:
канд. техн. наук, доц. К.В. Строганов (НИУ «МЭИ»);
д-р техн. наук В.С. Валавин


     Прибытков И.А.
П75 Теплофизика : учеб. пособие / И.А. Прибытков. - М. :
     Изд. Дом НИТУ «МИСиС», 2019. - 97 с.
        ISBN 978-5-907226-14-2



          This tutorial is for the Baccalaureate and Master Degrees students studying thermo-physics and heat engineering within their course of Metallurgy.
          The physical meaning of terms and definitions, and main units of measurements of the main quantities in thermo-physics are reviewed in this tutorial. This tutorial also features a brief review of the scientists who made a significant contribution towards the development of the related scientific disciplines.
          This tutorial may also be helpful for the Baccalaureate and Master Degrees students of other disciplines.

          Рассмотрены физический смысл терминов, определений и размерность основных теплофизических величин. Приведены краткие биографические очерки ученых, внесших существенный вклад в развитие теории рассматриваемого направления науки.
          Предназначено для обучающихся в бакалавриате и магистратуре по направлению подготовки 22.03.02, 22.04.02 «Металлургия», изучающих теплофизические и теплотехнические курсы. Может быть полезно студентам других направлений бакалавриата и магистратуры.

    УДК 669.04


ISBN 978-5-907226-14-2

© И.А. Прибытков, 2019
© НИТУ «МИСиС», 2019

TABLE OF CONTENTS

Introduction                                               4
1. Historical review of heat studies development ..........   6
2. Energy, heat, temperature, entropy                      15
3. Main units of the International System of Units (SI) ...  22
4. Conversion Factors of units of measurement of physical quantities ....................................  23
5. Heat transfer through thermal conduction ...............  29
6. Thermal convection - convective heat transfer...........43
7. Thermal radiation ..................................... 60
8. Similarity criteria (similarity numbers) .............. 71
9.  Outstanding scientists who made a significant contribution in development of the theory of hydrogasdynamics
and thermophysics ........................................ 77

3

INTRODUCTION





   Baccalaureate and Master Degrees students reading Metallurgy study various disciplines of thermo-physics and heat engineering. The scientific and technical content of these disciplines is complex and requires a good basic knowledge in mathematics, physics and other related subjects of a technical education. These disciplines use a large number of terms and definitions that carry a certain physical significance. Often textbooks, educational and methodological, as well as other publications, do not pay close attention to the content part of the terms and definitions, which may lead to incomprehension of the learning materials, a difference in interpretation, and eventual difficulties in communication with other specialists in their professional areas.
   This tutorial contains generalization and set interpretation of the terms, definitions and various thermo-physical values with their units of measurement, which are consistent with the International System of Units (SI). English language equivalent is presented for ease of using English language publications. In addition, this tutorial contains the list of the most used quantities with their units of measurement and conversion techniques from the earlier used systems of measurement. In the conclusion part of this tutorial, there is a brief biographical review, albeit not complete, of the scientists who made a significant contribution into establishing and the development of the scientific notions and provisions, which use the terms and definitions described in this tutorial. The author believes that inclusion of this material will allow the students to open up their mind and will, to a certain degree, motivate them to study this educational material.
   Formulae and reference data used for calculations are deliberately not included in this tutorial as they are outside the scope and the aim of this tutorial.
   This tutorial may also be helpful for the Baccalaureate and Master Degree students of other disciplines, which require knowledge in the areas of heat engineering.

   The author would like to express a special gratitude and appreciation to Larissa Pribytkova Manson Hart, Master of Physics and Mathematics, for her tireless work in editing the English version of the manuscript.
   The author would also like to thank engineer S.N. Mayko for her work in preparing the manuscript for publishing.

5

1. HISTORICAL REVIEW
OF HEAT STUDIES DEVELOPMENT





   The term “heat“ has been used from the pre-scientific era to describe properties of “hot” and “cold” without any quantitative measurements, while the term “temperature” had a qualitative meaning. The necessity of quantification of temperature, i.e. the necessity to tie it to the unit of measure and a number, came much later with scientific development. It became necessary to develop temperature scales and thermometers - devices for measuring temperature. This is considered to be the first step in the development of studies of heat. Galileo Galilei (15641642), Evangelista Torricelli (1608-1674), Otto von Guericke (1602-1686) and other outstanding scientists of that time made significant contributions to the heat studies development. However, Daniel Gabriel Fahrenheit (1686-1736), the inventor and creator of the thermometer, used until now, is considered to be a pioneer and a founding father of thermometry.
   Historically scientific circles considered heat as caloric (caloric - from the Latin word “calor” - heat). It was thought that caloric contained in all bodies and the temperature depended on the quantity contained in such a body. The fact that the temperature of bodies in the thermal contact state equalizes was considered to be an analogy with the balancing of the liquid level in communicating vessels.
   The next step in development of heat studies was made by Joseph Black (1728-1799). Black and his contemporaries considered heat to be an indestructible, non-creatable substance. In the beginning nobody recognised that even in the case of a steam engine created by James Watt (1736-1819), which in 1770 became the driving force of the Industrial Revolution, the heat was partially converted into mechanical work, which therefore resulted in the heat loss. It was only after the discovery of equivalent of heat and energy, made in 1842 by Julius von Mayer (1814-1873), Rudolf Clausius (1822-1888) established the second law of thermodynamics. 6

Clausius based his work on the genius theory of Sadi Carnot (17961832), who suggested that the work of steam engine is determined by the caloric (heat) transportation from the higher to the lower temperatures. The theory of caloric, as formulated by Joseph Black, could explain a large number of phenomena. However, there were certain difficulties in explaining many physical processes. For example, it is well known that if ice is heated, its temperature does not increase until the entire quantity of ice is melted. Black called this type of heat as “latent or hidden” (the term “latent heat of melting” is still used now), meaning that during the melting of the ice, heat is somehow transformed into water particles. Water holds large quantity of latent heat, therefore when an American scientist Sir Benjamin Thompson (Count Rumford, 1753-1814) established that the weight of melting ice stays unchanged, it was decided that caloric is weightless.
   Rumford conducted another experiment at the arsenal in Munich whereby he used the cannon boring tool to generate a large quantity of heat with a low quantity of metal shavings: he used a specially blunted tool to bore the cannon for two and a half hours. Rumford concluded that his experiment had proven that such heat generation was incompatible with the caloric theory, therefore invalidating this theory. However, his opponents argued that matter contained a lot of caloric, and even while boring with a blunt tool only a small quantity of it was released.
   Using the concept of temperature and indestructibility of the heat quantity, Jean-Baptiste Biot (1774-1862) in 1804, and in a more complete format Jean-Baptiste Joseph Fourier (1768-1830) in 1807 and 1811, founded the mathematical theory of thermal (heat) conduction.
   Chemical scientists considered that heat is a specific matter called caloric. Such fluid would have a special connection with the light and, in contact, would transfer some special “heating power” to the light.
   Sir Humphry Davy (1778-1829) was a strong opponent of materiality of heat and caloric hypothesis. Through his experiments of melting pieces of ice by rubbing them together, he finally disproved the caloric hypothesis and suggested the oscillating (wave) theory of heat. Thomas Young (1773-1829) supported

7

the wave theory of heat claiming that heat was the vibration of particles and such vibrations transmitted through space in the form of waves. Later (in 1807) he came to the conclusion that heat and light have the same vibration with the only difference being that the heat vibration velocity is lower than that of light.
   Caloric theory dominated till approximately 1850. However Democritus, known as the founder of the atomic theory, had suggested another hypothesis over 2000 years before: if a substance consists of tiny particles, then the difference between a solid and liquid substance is the strength of cohesion between such particles. If it is assumed that in the beginning the particles of a solid body move faster when heated, while remaining in the same place, then it is reasonable to assume that when reaching a certain temperature, these particles would break away from their position, thus forming a liquid, and with further heating there will be the next transformation - liquid will turn into gas. Galileo Galilei made a similar assumption in 1623, while in 1644 Descartes wrote that heat and cold were nothing but acceleration and deceleration of material particles. Newton, having differed with Descartes on nearly every issue, was in agreement with him on this particular matter.
   It is well known that moving bodies, experiencing friction, generate heat, and vice versa, heat produces motion as it happens, for example, in a steam engine or internal combustion engine. The question arises: how much work would a heat engine produce if supplied with a certain quantity of heat? It is rather difficult to answer this question and the following two important factors would need to be considered.
   First, when a heat engine produces some work, a certain amount of heat is lost.
   Sadi Carnot, a French physicist and a pioneer in this area, used the term “motive power” when talking about mechanical work. In his notebook discovered in 1878 after his death, Carnot was talking about heat as a vibrational motion of particles. He continued that if the assumption were correct, then the quantity of heat was nothing else but the quantity of mechanical energy used to make those particles move. He came to the conclusion that a general rule could be formulated, that the quantity of motive power was unchanged, in

8

other words it was not created nor could it be destroyed. This is one of the most important principles of physics - law of conservation of energy, or for the purposes of this chapter - the first law of thermodynamics.
   The word “energy”, first introduced in 1807 by T. Young, has the meaning of “complete quantity of energy” that remains constant and includes heat, kinetic and other forms of energy that are mentioned in scientific publications. In simple terms, energy can be defined as ability to produce work, while the quantity of mechanical work that the energy is equivalent to, can be considered as its measurement, regardless of the form of energy. Carnot managed to find a numerical value of the relationship between the quantities of work and heat energy; in modern units it is 3.7 J (joule) equals 1 cal (calorie) (4.19 is a more precise value).
   A German physicist J. Mayer made the same discovery when he noticed the difference in metabolic rate of the sailors traveling in equatorial waters. In 1842 Mayer established that the numerical value of the mechanical equivalent of heat was 3.85 joule, however his main achievement was his intuitive understanding of the importance and versatility of this new principle, which allowed him to apply the law of conservation of energy in various scientific areas such as physiology, celestial mechanics and the theory of tides.
   James Joule (1818-1889) however made the most significant contribution into the theory of conservation of energy. In 18431848 he carried out a series of experiments converting various types of energy: electric, heat, mechanical and internal. Based on the results he came to a conclusion that the mechanical equivalent of heat was between 4.25 and 4.60. Careful measurements taken by Joule had given additional support and an undisputable argument to the opponents of the caloric theory, which eventually got overturned: heat, as a type of energy, can be appear and disappear, however the total quantity of energy in the universe remains unchanged.
   It took a long time to establish the first law of thermodynamics due to the existence of another principle limiting the amount of work, which can be produced with a given quantity of heat. This principle was also discovered by Carnot and described in his paper “Reflections on the Motive Power of Fire” (1824). In this

9

work Carnot demonstrated that if T1 is a temperature of the heat transmitted into an engine, and T2 - temperature of the heat removed from the same engine, there exists a maximum amount of work (maximum efficiency) that such engine can produce using the supplied quantity of heat. This maximum quantity would always be lower than the total quantity of heat and can be determined only by the quantity of T₁ and T₂, regardless of the type of the media transferring this heat. Based on the law of conservation of energy it can be concluded that part of the heat transmitted into an engine gets removed out of the engine together with utilized material carrier, and remains unutilized. The lower the temperature of the material carrier, the harder it is to use the heat energy to produce work. For example, 1 kilogram of water at room temperature contains more heat than 10 grams of steam, however it is easier to extract energy from the latter. Therefore, as a result of conversion of energy into work a certain quantity of “useful” energy is removed together with material carrier, and there is no process that can increase the “usefulness” of such energy.
   R. Clausius introduced a mathematical version of this principle and introduced the concept of entropy, the name given by him, which is the quantity of “uselessness” of energy (from the point of view of producing work). Any process of conversion of heat into work is accompanied by increasing of entropy in the environs. It has been established that any attempt to decrease entropy leads to its increase in another place. This principle is now called the second law of thermodynamics. Clausius summarized the content of his paper with two following lines at the end of it:

    The energy of the universe is constant.
    The entropy of the universe tends to a maximum

   This maximum is attributed to the state when all matter will have the same temperature and there will be no useful energy. However, long before this state is reached, any form of life will be impossible. A rather pessimistic intellectual climate prevailing at the end of the 19th century is largely to do with the discovery of these two absolute limitations for the mankind.
   The study of thermodynamics, which was first developed in the works by Clausius, William Thomson (1st Baron Kelvin) (1824
10

1907) and their followers, succeeded in establishing connections between many physical and chemical phenomena based on the first and the second laws of thermodynamics, however there were some limits beyond which such general propositions were no longer enough to provide an explanation. It became necessary to establish the size of the substance particles and how they moved. Without this knowledge, for example, it is impossible to predict the melting temperature of a particular solid substance, its latent heat of melting and electrical properties. It became imperative to include certain laws that govern the motion of individual molecules into the general idea and notions of the thermodynamics. The problem that the scientists faced dealing with this task was much more complex and difficult than before. Molecules are very small in size making it impossible to observe directly, therefore any conclusions could only be drawn based on the general properties of the system consisting of billions of particles.
   Daniel Bernoulli (1700-1782) made the first steps in creating the kinetic molecular theory (kinetic theory) in his book on hydrodynamics (Hydrodynamica sive de viribus et motibus fluidorum commentarii, 1738). Bernoulli described gas as a large number of submicroscopic particles, which were in rapid free motion, if to disregard some collisions. Such particles constantly collide with the walls of a container, and while each individual collision is insignificant, a large number of such collisions would manifest itself as constant pressure. Thereafter, through further reasoning and implicitly using Newton laws, Bernoulli came to the conclusion that if gas was slowly compressed without changing the velocity of moving particles, then pressure would increase in such a way that the product of pressure and volume would remain constant. This is the very same correlation for gas being compressed at constant temperature, which was first empirically discovered by Robert Boyle (1627-1691). In 1660 Bernoulli also indicated that heating of a gas should lead to an increase in the velocity of particles and, therefore, to an increase in pressure due to the increase in frequency and force of particles colliding with the walls of a container. A Russian scientist Mikhail V. Lomonosov (1711-1765) expressed similar ideas nine years later, in addition he also stated that if in principle there was no upper limit for the

11