06 Exchanging Thermal Energy

1 EXCHANGING THERMAL ENERGY What is energy? All through the Science courses the word “energy” appears repeatedly. Although there are mathematical expressions that clearly define different classes of energy, the concept of energy itself has been a little diffuse: you were never told the physical meaning of the term “energy”. From a mechanical point of view energy is the possibility that a system has to do some work. So What’s Work? Work is done by a force that moves along a path changing the speed of an object. Jimmy pushing a cache is working. Friction of the floor against the cache is working too: as Jimmy speeds up the cache, friction “eats up” Jimmy’s effort stopping the cache simultaneously. The gravitational force on a falling object and the electric forces that drive the electrons along a wire (an electric current) are working. Steam expanding inside the piston of a steam engine is working too. Dynamite exploding in a tunnel is also working on the stones and air around it. Instead, Hercules holding a boulder on his shoulders is not working (no distance moved). The gravitational force of the Earth on the Moon is not working either (there’s no change in speed). Work is calculated as the force on the object times the distance it moved and the unit of work is the unit of force times the unit of distance.

When Jimmy makes a force of 100 N on the cache along a 5 m path he is working: The work done will be: 100 N x 5 m = 500 J (the symbol for Joule is J). If there were no friction, the cache would be rushing forwards and now the cache would be able to do some work (for example colliding against another object and making it move). Before Jimmy’s push the cache was not moving and could do nothing but stand there. Now the cache has energy. Jimmy has transferred energy to the cache by means of the work done. Thus, work is just energy being transferred from one object to another one by means of moving forces. Consequently the unit of energy is the Joule too. Two Classes of Energy There are several different sources of energy (waves, sun, dams, fuels, wind, atomic nuclei) but just two classes of it: kinetic and potential energies.

2 Kinetic energy (kinesis is a Greek word for movement) is related to the speed of an object and its mass: the faster an object moves, the more energy it has. It is more difficult to stop a car running at 100 km/hr than if it just crawls at 2 km/hr. Similarly, the more massive an object is, the more energy it has as it moves: a motor must do more work to speed a car than a motorbike from rest to 50 km/hr. Although you will not use it the equation to calculate the kinetic energy of an object goes like this:

Potential energy (comes from Aristotle’s concept of potency, something that is there, a possibility but not actually acting) is related to forces and relative positions. There is a specific equation to calculate the potential energy depending on the class of forces involved: gravitational potential energy, elastic potential energy, electric potential energy). In all of them forces and distances are included. This is the equation to calculate the gravitational potential energy (not to be used):

Thermal Energy and the Particle Theory According to the particle theory, matter is made of sub-microscopic particles that move constantly in empty space. Even in the solid state, the particles vibrate frantically. In liquids and gases these particles move randomly, in liquids sliding past each other and in gases separated by distances about 10 times longer their size. If particles move, they have kinetic energy; not all of them have the same energy but most of them have energies around an average value that is directly linked with the macroscopic property of objects that we call “temperature” The outer part of the particles is formed by the electrons in the outer shell of their atoms. These electrons are not evenly distributed (remember electronegativity and polar molecules) and this gives way to electrical interactions among them. In fact, these are the forces that are responsible for the existence of the liquid and solid states! This means that particles have potential energy too. This potential energy comes from electric forces that are amazingly stronger than gravitational forces. The grand total obtained by adding all the individual kinetic and potential energies of each and every particle in a system is called the Internal or Thermal Energy of the system. Thermal Energy is the total (energy and potential) energy of a system randomly distributed among its particles The Meaning of Heat. When two systems at different temperatures (that is in which their particles are moving at different speeds in average) are put in contact, their particles will collide and transfer energy from one system to the other reciprocally. As time passes kinetic energy will be evenly distributed on both objects what means that they will be at the same temperature.

3 This is a microscopic explanation of what happens when two objects at different temperatures get to thermal equilibrium (no more changes observed): the particles have done “mini works” (“mini energy transfers”) on each other. Before the particle theory had been fully established, everybody knew that two objects at different temperatures tend to change to an intermediate stable situation called thermal equilibrium. One of the systems at higher temperature would transfer “something” to the other one at a lower temperature until both temperatures got levelled. This “something” was called heat long before the concept of energy had been developed. The unit of heat was called the calorie: one calorie (symbol cal) was defined as the amount of heat that has to be given to 1 gram of water to raise its temperature from 14 ºC to 15 ºC. A bigger unit called the kilocalorie or “big” calorie (symbol Cal) was also defined (changing “grams” for kilograms) Considering now the grand total of the mini energy transfers is what from a macroscopic point of view has been called heat. Properly defined, heat is thermal (internal) energy transferred by means of a temperature difference. Heat / Energy Equivalences The scientist that found the equivalence between the units of mechanical energy with heat was James Prescott Joule and after him the energy unit has been named.

You can find the energetic content of many foods both in Cal (kcal) and kJ in their packaging. Try with cookies, cereals, etc. A word about this energy content: the amount of energy in foods (in fact it is chemical energy, a class of potential energy stored in the chemical bonds) is in an absolute different scale when compared with mechanical energy. You will be amazed at finding how food energy and mechanical energy compare.

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Heating Curves All through the following discussion we will assume that substances are thermally stable, that is, they will suffer no chemical change with increasing temperature. Suppose heat is given regularly to a substance (ice) by means of an energy source (e.g. a burner). At the same time the temperature of the system is recorded at regular intervals. Finally a temperature/time graph is plotted using the data collected. The graph would look as shown below

There are five stretches shown. Two of them are flat lines the other three sloped straight lines. This kind of curve is called a heating curve. In segments AB, CD and EF as heat is given to the system the temperature rises. It can be seen that the temperature change is directly proportional to the amount of heat given. In these segments water is found as ice, liquid water or steam (water vapour) only one physical state at a time. On the other hand, in the flat segments BC and DE water appears simultaneously in two physical states at the same time. At these two temperatures a change of state is taking place. Specific Heat (Specific Heat Capacity) We can repeat this experiment using different masses of ice and we will find that the more mass we use, the smaller the temperature change: this means that the change in temperature is inversely proportional to the mass being heated. Recalling the proportionality between amount of heat supplied and temperature change and using symbols:

ΔT stands for change in temperature, Q stands for amount of heat supplied and m for the mass being heated. The proportionality constant is different for different substances and is called the specific heat or specific heat capacity and its symbol is “c”. We can rewrite the previous proportion as an equation using the proportionality constant:

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Specific heat can be defined as the amount of heat required to raise 1 ºC the temperature of 1 gram of a substance. The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C which is higher than any other common substance. As a result, water plays a very important role in temperature regulation. The specific heats of several substances are shown in the chart to the right:

Thermal (Heat) Capacity Heat or thermal capacity is the amount of heat required to raise the temperature of any mass of a substance 1 ºC

Latent Heat Can a substance being heated without its temperature being raised? Indeed, that is what happens as a substance is changing its physical state. During these phase transitions, the thermal energy (heat) supplied to the substance is used to overcome the attractive electric forces that keep the particles together. Hence this energy will be stored as potential energy but the particles will have the same movement energy (kinetic energy) as before. To melt 1 g of ice (assuming it is already at 0ºC) 80 cal are needed! This is the same amount of energy that will be needed to rise the temperature of this gram of water up to 80 ºC. To completely separate the particles from each other (vaporising) the amount of energy is almost seven times greater: 540 cal per gram of vapour formed. This is called the “latent” heat and symbolised as “L”. Latent heat can be either heat of vaporisation or heat of fusion. In this case as there is no change in temperature the equation turns into:

The units for latent heats are cal/g. (J/g). Some latent heats are shown in the chart. Heat Conduction Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If one end of a metal rod is at a higher

6 temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. Heat conductivity is different for different substances: metals are very good heat conductors but rubber, wood or plastics are not. The chart to the right shows the thermal conductivity for several materials: which are the reasons for the wide variations in thermal conductivity? Gases are poor conductors. Their thermal conductivity is low compared to most solids since their particles are wide apart and heat transmission by direct collisions between molecules will not be as frequent as in solids or liquids. Non-metallic solids transfer heat by lattice vibrations so that there is no net motion of the media as the energy propagates through. They are not very good conductors either. Many different materials are used as thermal insulators to avoid systems to either cool down (Pizza delivery) or warming up (ice cream delivery) Liquids are usually in an intermediate situation because their particles are close to each other but not as close as in solids. Metals are much better thermal conductors than non-metals because the same mobile electrons which participate in electrical conduction also take part in the transfer of heat. Newton’s cooling (and heating) law. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is:

In this equation Q/t stands for the joules per unit time that are conducted from the hot to the cold system (in joules per second, frequently called watts) A is the contact area between the two systems (in m2), d is the thickness of the wall (in m) that separates both systems and (Thot - Tcold) is the temperature difference between the systems (in degrees Celsius or Kelvin). The Greek letter “kappa” κ is a property of the wall called its thermal conductivity

7 Heat Convection Heat conduction in fluids (gases or liquids is not an importance mechanism for energy transfer. In fluids, because of thermal expansion and gravity, massive movement of particles take place in a process called convection. Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises. Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.

Air is a very poor conductor but it easily forms convective currents. That will carry heat away. Walls built with “hollow” bricks will show better insulating properties than solid walls. But if the bricks are stuffed with Styropor (Telgopor) insulation will be improved several times. This is because Styropor is basically made of air “trapped” in tiny cells preventing air to escape and consequently the heat energy to fly away. For the same reason thick woollen blankets keep us warm in winter. We are the source of heat but the blanket will keep the air warmed by our own energy trapped between the woollen threads of the fabric. Convection can also lead to circulation in a liquid, as in the heating of a pot of water over a flame. Heated water expands and becomes more buoyant. Cooler, denser water near the surface descends and patterns of circulation can be formed, though they will not be as regular as suggested in the drawing.

In ordinary heat transfer on the Earth, it is difficult to quantify the effects of convection since it inherently depends upon small nonuniformities in an otherwise fairly

8 homogeneous medium. In modelling things like the cooling of the human body, we usually just lump it in with conduction. Radiation There is a third mechanism for heat transmission: radiation. Heat travels through empty space from the sun to us exclusively by radiation. Radiation moves through the empty spaces among the particles of the atmosphere (of any gas actually) and hits the ground or the sea where it is absorbed (there’s not too much empty space in liquids and solids). Thus, the surface of the earth gets hot and in turn heats the lower layers of the atmosphere by conduction. Hot air expands and being “lighter” convective currents are formed that will distribute the energy all around the Globe. Hot Radiative phenomena involve also the transmission of radio waves, light and cosmic rays. We will deal with it in the next unit. QUESTIONS AD PROBLEMS 1- Nutritional information for “Frutigran” biscuits states that a three biscuit serving contains150 kcal (150 Cal). How many kilojoules and joules does a serving provide? 2- Calculate the kinetic energy of a Chevrolet Corsa. (1030 kg) plus its 70 kg driver, both travelling at 33,4 m/s (120 km/hr). Compare with problem (1) 3- Benzene freezes at 5 ºC and boils at 78 ºC. sketch the shape of a heating curve for benzene. 4- Calculate the amount of heat required to heat from 10 ºC to 60 ºC: a- 10 g of water b- 10 g of copper c- 10 g of sand d- Can you explain the temperature difference between sand and water on a sunny day? 5- A 50 g block of steel at 100 ºC is added to a certain mass of ice at 0 ºC until it cools down to that temperature. The heat interchanged is all absorbed by ice. a- How much heat was delivered to ice? b- How many grams of ice were melted by that amount of heat? 6- Which of these two produces the most harmful burn boiling water at 100 ºC or steam at the same temperature? Give reasons for your answer. 7- The so called “radiators” actually heat the air in a room by conduction 8- Explain why the heating element in an electric kettle is placed at the bottom and never at the top. 9- Why do birds have all their body covered with feathers if they just use their wings to fly? 10- Freezers in a supermarket never have hinged top lids. They may have a sliding cover or even be open with no cover at all. Why is this not anti-economic? 11- A house has a 12 m2 wooden wall 5 cm thick. If the outer surface is at 0 ºC and the inner surface at 20 ºC: how many joule per second (watts) are lost through the wall? 12- Repeat exercise (10) but for a glass wall of the same dimensions.