Heat and Kinetic Theory PDF

Heat and Kinetic Theory The sensation of hotness is certainly familiar to all of us. We know from experience that when two bodies, one hot and the other cold, are placed in an enclosure, the hotter body will cool and the colder body will heat until the degree of hotness of the two bodies is the...

Heat and Kinetic Theory The sensation of hotness is certainly familiar to all of us. We know from experience that when two bodies, one hot and the other cold, are placed in an enclosure, the hotter body will cool and the colder body will heat until the degree of hotness of the two bodies is the same. Clearly something has been transferred from one body to the other to equalize their hotness. That which has been transferred from the hot body to the cold body is called heat. ‫الصور عن‬ Heat and‫بحث‬ Kinetic ‫نتيجة‬ Theory  Heat may be transformed into work, and therefore it is a form of energy. Heated water, for example, can turn into steam, which can push a piston. In fact, heat can be defined as energy being transferred from a hotter body to a colder body. In this part, we will discuss various properties associated with heat. We will describe the motion of atoms and molecules due to thermal energy.  Kinetic Theory of Matter To understand the present-day concept of heat, we must briefly explain the structure of matter. Matter is made of atoms and molecules, which are in continuous disordered motion. In a gas, the atoms (or molecules) are not bound together. They move in random directions and collide frequently with one another and with the walls of the container. ‫الصور عن‬ Kinetic Theory ‫نتيجة بحث‬ of Matter  ‫الصور عن‬ Kinetic Theory ‫نتيجة بحث‬ of Matter In addition to moving linearly, gas molecules vibrate and rotate, again in random directions. In a solid, where the atoms are bound together, the random motion is more restricted. The atoms are free only to vibrate and do so, again randomly, about some average position to which they are locked. The situation with regard to liquids is between these two extremes. Here the molecules can vibrate, but they also have some freedom to move and to rotate.  Because of their motion, the moving particles in a material possess kinetic energy. This energy of motion inside materials is called internal energy, and the motion itself is called thermal motion. What we have so far qualitatively called the hotness of a body is a measure of the internal energy; that is, in hotter bodies, the random motion of atoms and molecules is faster than in colder bodies. Therefore, the hotter an object, the greater is its internal energy. The physical sensation of hotness is the effect of this random atomic and molecular motion on the sensory mechanism. Temperature is a quantitative measure of hotness. The internal energy of matter is proportional to its temperature.  ‫الصور عن‬ kinetic energy ‫نتيجة بحث‬ of matter and temperature ‫الصور عن‬ kinetic energy ‫نتيجة بحث‬ of matter and temperature ‫الصور عن‬ kinetic energy ‫نتيجة بحث‬ of matter and temperature  Using these concepts, it is possible to derive the equations that describe the behavior of matter as a function of temperature. Gases are the simplest to analyze. The theory considers a gas made of small particles (atoms or molecules) which are in continuous random motion. Each particle travels in a straight line until it collides with another particle or with the walls of the container. After a collision, the direction and speed of the particle is changed randomly. In this way kinetic energy is exchanged among the particles.  The colliding particles exchange energy not only among themselves but also with the wall of the container. For example, if initially the walls of the container are hotter than the gas, the particles colliding with the wall on the average pick up energy from the vibrating molecules in the wall. As a result of the wall collisions, the gas is heated until it is as hot as the walls. After that, there is no net exchange of energy between the walls and the gas. This is an equilibrium situation in which, on the average, as much energy is delivered to the wall by the gas particles as is picked up from it.  The speed and corresponding kinetic energy of the individual particles in a gas vary over a wide range. Still it is possible to compute an average kinetic energy for the particles by adding the kinetic energy of all the individual particles in the container and dividing by the total number of particles. Many of the properties of a gas can be simply derived by assuming that each particle has this same average energy. ‫ الصور عن‬kinetic average ‫نتيجة بحث‬ energy for the particles ‫الصور عن‬ gas in container ‫نتيجة بحث‬  The internal energy in an ideal gas is in the form of kinetic energy, and therefore the average kinetic energy is proportional to the temperature. The proportionality can be changed to an equality by multiplying the temperature T by a suitable constant which relates the temperature to the internal energy. The constant is designated by the symbol k, which is called Boltzmann constant. For historical reasons, Boltzmann constant has been so defined that it has to be multiplied by a factor of 3/2 to relate temperature to the average kinetic energy of a molecule; thus,  The temperature in this equation is measured on the absolute temperature scale in degrees Kelvin. The size of the degree division on the absolute scale is equal to the Celsius, or centigrade, degree, but the absolute scale is transposed so that 0◦C=273.15 K. Since our calculations are carried only to three significant figures, we will use simply 0◦C=273 K. The value of Boltzmann constant is The velocity defined by last equation in last slit is called thermal velocity. ‫بحث الصور عن‬ absolute temperature ‫نتيجة‬ scale ‫بحث الصور عن‬ absolute temperature ‫نتيجة‬ scale ‫بحث الصور عن‬kelvin temperature ‫ نتيجة‬to celsius ‫بحث الصور عن‬kelvin temperature ‫ نتيجة‬to celsius ‫بحث الصور عن‬kelvin temperature ‫ نتيجة‬to celsius Example 1: On a day when the temperature reaches 50°F, what is the temperature in degrees Celsius and in kelvins? Example 2: A pan of water is heated from 25°C to 80°C. What is the change in its temperature on the Kelvin scale and on the Fahrenheit scale?  Each time a molecule collides with the wall, momentum is transferred to the wall. The change in momentum per unit time is a force. The pressure exerted by a gas on the walls of its container is due to the numerous collisions of the gas molecules with the container. The following relationship between pressure P, volume V, and temperature T, is derived in most basic physics texts: Here N is the total number of gas molecules in the container of volume V, and the temperature T, is again measured on the absolute scale.  ‫الصور عن‬ Gas law ‫نتيجة بحث‬ ‫نتيجة بحث الصور عن‬ PV=NKT In a closed container, the total number of particles N is fixed; therefore, if the temperature is kept unchanged, the product of pressure and volume is a constant. This is known as Boyle’s law. ‫الصور عن‬ ‫‪Gas‬‬ ‫‪law pv=nkt‬‬ ‫نتيجة بحث‬ Example 3: An ideal gas occupies a volume of 100 cm3 at 20°C and 100 Pa. Find the number of moles of gas in the container. Example 4: Gas is contained in an 8.00-L vessel at a temperature of 20.08C and a pressure of 9.00 atm. (a) Determine the number of moles of gas in the vessel. (b) How many molecules are in the vessel?. Example 5: An auditorium has dimensions 10.0 m x 20.0 m x 30.0 m. How many molecules of air fill the auditorium at 20.0 oC and a pressure of 101 kPa (1.00 atm)?  Unit of Heat Heat is measured in calories. One calorie (cal) is the amount of heat required to raise the temperature of 1 g of water by 1 C◦. Actually, because this value depends somewhat on the initial temperature of the water, the calorie is defined as the heat required to raise the temperature of 1 g of water from 14.5◦C to 15.5◦C. ‫نتيجة بحث الصور عن‬ heat One calorie is equal to 4.184 J. In the life sciences, heat is commonly measured in kilocalorie units, abbreviated Cal; 1 Cal is equal to 1000 cal.  Transfer of Heat Heat is transferred from one region to another in three ways: by conduction, convection, and radiation. ‫الصور عن‬ Heat is transferred ‫نتيجة بحث‬ Heat Transfer ‫بحث الصور عن‬ conduction by‫نتيجة‬ radiation  Conduction If one end of a solid rod is placed in the proximity of a heat source such as a fire, after some time the other end of the rod will become hot. In this case, heat has been transferred from the fire through the rod by conduction. The process of heat conduction involves the increase of internal energy in the material. The heat enters one end of the rod and increases the internal energy of the atoms near the heat source. ‫الصور عن‬ heat is transferred ‫ نتيجة بحث‬by conduction  ‫الصور عن‬ heat is transferred ‫ نتيجة بحث‬by conduction In a solid material, the internal energy is in the vibration of the bound atoms and in the random motion of free electrons, which exist in some materials. The addition of heat increases both the random atomic vibrations and the speed of the electrons. The increased vibration motion is transferred down the rod through collisions with neighboring atoms. However, because the atoms in the solid are tightly bound, their motion is restricted. Therefore, heat transfer via atomic vibrations is slow.  In some materials, the electrons in the atoms have enough energy to break loose from a specific nucleus and move freely through the material. The electrons move rapidly through the material so that, when they gain energy, they transfer it quickly to adjacent electrons and atoms. In this way, free electrons transfer the increase in the internal energy down the rod. Materials such as metals, which contain free electrons, are good conductors of heat; materials such as wood, which do not have free electrons, are insulators. The amount of heat Hc conducted per second through a block of material is given by: Here A is the area of the block, L is its length, and T1 −T2 is the temperature difference between the two ends. The constant Kc is the coefficient of thermal conductivity. In physics texts, Kc is usually given in units of cal cm/sec.cm2.C◦.  However, for problems involving living systems, it is often more convenient to express Kc in units of Cal cm/m2.hr.C◦. This is the amount of heat (in Cal units) per hour which flows through a slab of material 1 cm thick and 1 m square per C◦ temperature difference between the faces of the slab. The thermal conductivity of a few materials is given in next table. Example 6: k1 and k2 are in thermal contact with each other, as shown in next figure. The temperatures of their outer surfaces are Tc and Th , respectively, and Th>Tc. Determine the temperature at the interface and the rate of energy transfer by conduction through the slabs in the steady-state condition. Example 7: A person walking at a modest speed generates heat at a rate of 280 W. If the surface area of the body is 1.5 m2 and if the heat is assumed to be generated 0.03 m below the skin, what temperature difference between the skin and interior of the body would exist if the heat were conducted to the surface? Assume the thermal conductivity is the same as that for animal muscle, 0.2 W/m.K. Hc = 280 W k = 0.2 W/m.K L = 0.03 m ΔT1 = ??? A = 1.5 m2 Example 8: A copper hot-water pipe is 2 m long and 0.004 m thick, and has a surface area of 0.12 m2. If the water is at 80 ͦ C and the temperature in the room is 15 ͦ C, at what rate is heat conducted through the pipe wall? Hc = ??? W k = 400 W/m.K L = 0.004 m ΔT = 65 K A = 0.12 m2 ‫صورة ذات صلة‬ Example 9: For human body, Calculate the rate of heat transfer by conduction from the core to skin through the fat layer of thickness 3 cm, as the skin temperature is 35 oC and the core is 37 oC, while the body area is 1.5 m2? Assume the thermal conductivity of the fat equal 0.25 W/m.K. Hc =???? W k = 0.25 W/m.K L = 3 cm T1 = 37 oC T2 = 35 oC A = 1.5 m2  Convection In solids, heat transfer occurs by conduction; in fluids (gases and liquids), heat transfer proceeds primarily by convection. When a liquid or a gas is heated, the molecules near the heat source gain energy and tend to move away from the heat source. Therefore, the fluid near the heat source becomes less dense. Fluid from the denser region flows into the rarefied region, causing convection currents. These currents carry energy away from the heat source.  ‫الصور عن‬ heat by convection ‫نتيجة بحث‬ ‫الصور عن‬ heat by convection ‫نتيجة بحث‬ ‫الصور عن‬ heat by convection ‫نتيجة بحث‬ ‫الصور عن‬ heat by convection ‫نتيجة بحث‬  When the energetic molecules in the heated convection current come in contact with a solid material, they transfer some of their energy to the atoms of the solid, increasing the internal energy of the solid. In this way, heat is coupled into a solid. The amount of heat transferred by convection per unit time H′c is given by Here A is the area exposed to convective currents, T1 −T2 is the temperature difference between the surface and the convective fluid, and h is the coefficient of convection, which is usually a function of the velocity of the convective fluid. ‫نتيجة بحث الصور عن‬ CONVECTION thermal resistance Example 10: A naked person with a surface area of 1.8 m2, a skin temperature of 31⁰C and an average h of 7.1 W.m-2.K-1 loses 126 W by convection. What is the air temperature surrounding him? H′c = 126 W h = 7.1 W.m-2.K-1 T1 = 31+273 K T2 = ??? A = 1.8 m2 Example 11: In a warm room, a naked resting person has a skin temperature of 33 ͦ C. If the room temperature is 29 ͦ C and the body surface area is 1.5 m2, what is the rate of heat loss due to convection? H′c = ??? W h = 7.1 W.m-2.K-1 T1= 31 T2 = 29 A = 1.5 m2  ‫ الصور عن‬law fourier's ‫بحث‬of‫نتيجة‬ conduction resistance ‫بحث الصور عن‬ conduction thermal ‫ نتيجة‬resistance Thermo Flask ‫ الصور عن‬law fourier's ‫بحث‬of‫نتيجة‬ conduction resistance R - Thermo Resistance T- Temperature  Equivalent R Conduction Convection R= 1/(hA) R= L/(kA) ‫الصور عن‬Flask Thermo ‫نتيجة بحث‬ LAYER Example 12: An electric hot plate is maintained at a temperature of 300 oC, and is used to keep a solution just boiling at 90 oC. The solution is contained in an enameled cast iron vessel of wall thickness 20 mm and enameled thickness 0.5 mm. The heat transfer coefficient for boiling solution is 1000 W/m2K and thermal conductivities of cast iron and the enamel are 40 and 1 W/mK, respectively. Calculate the rate of the heat transferred per unit area and the interference temperatures.  Radiation Vibrating electrically charged particles emit electromagnetic radiation, which propagates away from the source at the speed of light. Electromagnetic radiation is itself energy (called electromagnetic energy), which in the case of a moving charge is obtained from the kinetic energy of the charged particle. Because of internal energy, particles in a material are in constant random motion. Because the electrons are much lighter than the nuclei, they move faster and emit more radiant energy than the nuclei.  Both the positively charged nuclei and the negatively charged electrons vibrate and, therefore, emit electromagnetic radiation. In this way, internal energy is converted into radiation, called thermal radiation. Due to the loss of internal energy, the material cools. The amount of radiation emitted by vibrating charged particles is proportional to the speed of vibration. ‫بحث الصور عن‬ conduction by‫نتيجة‬ radiation Hot objects, therefore, emit more radiation than cold ones.  When a body is relatively cool, the radiation from it is in the long-wavelength region to which the eye does not respond. As the temperature (i.e., the internal energy) of the body increases, the wavelength of the radiation decreases. At high temperatures, some of the electromagnetic radiation is in the visible region, and the body is observed to shine. ‫بحث الصور عن‬ vibration of particle ‫ نتيجة‬and wavelength equation ‫بحث الصور عن‬ vibration of particle ‫ نتيجة‬and wavelength equation  When electromagnetic radiation impinges on an object, the charged particles (electrons) in the object are set into motion and gain kinetic energy. Electromagnetic radiation is, therefore, transformed into internal energy. The mount of radiation absorbed by a material depends on its composition. Some materials, such as carbon black, absorb most of the incident radiation. These materials are easily heated by radiation. ‫ بحث الصور عن‬effect photoelectric ‫نتيجة‬ Photoelectric Effect  Other materials, such as quartz and certain glasses, transmit the radiation without absorbing much of it. Metallic surfaces also reflect radiation without much absorption. Such reflecting and transmitting materials cannot be heated efficiently by radiation. ‫الصور عن‬black carbon ‫بحث‬electromagnetic ‫نتيجة‬ radiation  The rate of emission of radiant energy Hr by a unit area of a body at temperature T is Here σ is the Stefan-Boltzmann constant, which is 5.67×10−8 W/m2-K4 or 5.67×10−5 erg/cm2-◦K4-sec. The temperature is measured on the absolute scale, and e is the emissivity of the surface, which depends on the temperature and nature of the surface. The value of the emissivity varies from 0 to 1. Emission and absorption of radiation are related phenomena; surfaces that are highly absorptive are also efficient emitters of radiation and have an emissivity close to 1. Conversely, surfaces that do not absorb radiation are poor emitters with a low value of emissivity.  A body at temperature T1 in an environment at temperature T2 will both emit and absorb radiation. The rate of energy emitted per unit area is eσT14 , and the rate of energy absorbed per unit is eσT24. The values for e and σ are the same for both emission and absorption. If a body at a temperature T1 is placed in an environment at a lower temperature T2, the net loss of energy from the body is If the temperature of the body is lower than the temperature of the environment, the body gains energy at the same rate.  The intensity increases with increasing ‫نتيجة بحث الصور عن‬equation stefan-boltzmann temperature. The amount of radiation emitted increases with increasing temperature. The area under the curve The peak wavelength decreases with increasing temperature. Coal ‫بحث الصور عن‬ vibration of particle ‫ نتيجة‬and wavelength equation Example 13: A student is trying to decide what to wear. The surroundings (his bedroom) are at 20.0°C. If the skin temperature of the unclothed student is 35°C, what is the net energy loss from his body in 10.0 min by radiation? Assume that the emissivity of skin is 0.900 and that the surface area of the student is 1.50 m2. Net rate of energy loss from the whole skin is Total energy lost by the skin in 10 min Example 14: The person has a skin temperature of 33 ͦ C =306 K and was in a room where the walls were at 29 ͦ C =302 K. If the emissivity is 1 and the body surface area is 1.5 m2, what is the rate of heat loss due to radiation? Hr = ??? W σ = 5.67 x 10-8 W.m-2.K-4 T= 33 To= 29 A = 1.5 m2 e=1 Look at the three images below. Identify which is an example of conduction, convection, and radiation. A B C