A Level Physics: Thermal Physics (PDF)

# Thermal Physics ## 22.1 Internal Energy and Temperature When you are outdoors in winter, you need to wrap up well, otherwise energy is transferred by heating from your body to your surroundings. Your body loses energy, and your surroundings gain energy. In summer, if you are in a very hot room,...

# Thermal Physics ## 22.1 Internal Energy and Temperature When you are outdoors in winter, you need to wrap up well, otherwise energy is transferred by heating from your body to your surroundings. Your body loses energy, and your surroundings gain energy. In summer, if you are in a very hot room, you will heat up because of energy transferred to you from the room. Energy transfer between two objects takes place if - one object exerts a force on the other object and makes it move. In other words, one object does work on the other object. - one object is hotter than the other object, so energy transfer by heating takes place by means of conduction, convection, or radiation. In other words, energy is transferred by heating because of a temperature difference between two objects. ### Internal Energy The brake pads of a moving vehicle become hot if the brakes are applied for a long enough time. The work done by the frictional force between the brake pads and the wheel heats the brake pads,which gain energy from the kinetic energy of the vehicle. The temperature of the brake pads increases as a result, and the internal energy of each brake pad increases. As explained below, the internal energy of an object is the energy of its molecules due to their individual movements and positions. The internal energy of an object due to its temperature is sometimes called thermal energy. However, some of the internal energy of an object might be due to other causes. For example, an iron bar that is magnetised has more internal energy than if it is unmagnetised, because of the magnetic interaction between the iron bar's atoms. The internal energy of an object is increased because of: - energy transfer by heating the object, or - work done on the object, for example, work done by electricity. If the internal energy of an object stays constant, then either: - there is no energy transfer by heating and no work is done, or - energy transfer by heating and work done balance each other out. For example, the internal energy of a lamp filament increases when the lamp is switched on because work is done by the electricity supply pushing electrons through the filament. Because of this, the filament becomes hot. When it reaches its operating temperature, energy is transferred to the surroundings by heating, and the filament radiates light. Work done by the electricity supply pushing electrons through the filament is balanced by the energy transfer and light radiated from the filament. ### Learning Objectives - Define internal energy. - State the lowest temperature that is possible. - Demonstrate the first law of thermodynamics in action. ### The First Law of Thermodynamics In general, when work is done on or by an object and/or energy is transferred by heating, the change of internal energy of the object = the total energy transfer due to work done and heating This general statement is called the first law of thermodynamics and may be written as: Change of internal energy AU = Q + W where Q is the energy input to the system by heating and W is the work done ON the system. When it is applied to an object, the directions of the energy transfers (i.e., to or from the object) are very important and determine whether the overall internal energy of the object increases or decreases. ### About Molecules A molecule is the smallest particle of a pure substance that is characteristic of the substance. For example, a water molecule consists of two hydrogen atoms joined to an oxygen atom. An atom is the smallest particle of an element that is characteristic of the element. For example, a hydrogen atom consists of a proton and an electron. - In a solid, the atoms and molecules are held to each other by forces due to the electrical charges of the protons and electrons in the atoms. The molecules in a solid vibrate randomly about fixed positions. The higher the temperature of the solid, the more the molecules vibrate. The energy supplied to raise the temperature of a solid increases the kinetic energy of the molecules. If the temperature is raised enough, the solid melts. This happens because its molecules vibrate so much that they break free from each other and the substance loses its shape. The energy supplied to melt a solid raises the potential energy of the molecules because they break free from each other. - In a liquid, the molecules move about at random in contact with each other. The forces between the molecules are not strong enough to hold the molecules in fixed positions. The higher the temperature of a liquid, the faster its molecules move. The energy supplied to a liquid to raise its temperature increases the kinetic energy of the liquid molecules. Heating the liquid further causes it to vaporise. The molecules have sufficient kinetic energy to break free and move away from each other. - In a gas or vapour, the molecules also move about randomly but much further apart on average than in a liquid. Heating a gas or a vapour makes the molecules speed up and so gain kinetic energy. The internal energy of an object is the sum of the random distribution of the kinetic and potential energies of its molecules. Increasing the internal energy of a substance increases the kinetic and/or potential energy associated with the random motion and positions of its molecules. ## 22.2 Specific Heat Capacity ### Heating and Cooling Sunbathers on the hot sandy beaches of the Mediterranean Sea dive into the sea to cool off. Sand heats up much more readily than water does. Even when the sand is almost too hot to walk barefoot across, the sea water is refreshingly cool. The temperature rise of an object when it is heated depends on: - the mass of the object - the amount of energy supplied to it - the substance or substances from which the object is made. The specific heat capacity, c, of a substance is the energy needed to raise the temperature of unit mass of the substance by 1K without change of state. The unit of c is Jkg-¹K-1. ### Learning Objectives - Explain what is meant by heating up and by cooling down. - State which materials heat up and cool down the fastest. - Define and measure specific heat capacity. ### The Inversion Tube Experiment In this experiment, the gravitational potential energy of an object falling in a tube is converted into internal energy when it hits the bottom of a tube. The object is a collection of tiny lead spheres. The tube is inverted each time the spheres hit the bottom of the tube. The temperature of the lead shot is measured initially and after a particular number of inversions. Let m represent the mass of the lead shot. For a tube of length L, the loss of gravitational potential energy for each inversion = mgL. Therefore, for n inversions, the loss of gravitational potential energy = mgLn. The gain of internal energy of the lead shot = mcΔθ, where c is the specific heat capacity of lead and Δθ is the temperature rise of the lead shot. Assuming that all the gravitational potential energy lost is transferred to internal energy of the lead shot, mcΔθ = mgLn. Therefore, c = gLn/Δθ. So, the experiment can be used to measure the specific heat capacity of lead with no other measurements than the length of the tube, the temperature rise of the lead, and the number of inversions. ### Specific Heat Capacity Measurements using Electrical Methods #### Measurement of the Specific Heat Capacity of a Metal A block of metal of known mass _m_ in an insulated container is used. A 12V electrical heater is inserted into a hole drilled in the metal and used to heat the metal by supplying a measured amount of electrical energy. A thermometer inserted into a second hole drilled in the metal is used to measure the temperature rise ΔΘ (= its final temperature - its initial temperature). A small amount of water or oil in the thermometer hole will improve the thermal contact between the thermometer and the metal. The electrical energy supplied = heater current _I_ x heater p.d. _V_ x heating time _t_. So, assuming no heat loss to the surroundings, mcΔθ = IVt Therefore, c = IVt/mΔθ #### Measurement of the Specific Heat Capacity of a Liquid A known mass of liquid is used in an insulated calorimeter of known mass and known specific heat capacity. A 12V electrical heater is inserted into the liquid and used to heat it directly. A thermometer inserted into the liquid is used to measure the temperature rise, ΔΘ. - The electrical energy supplied = current _I_ × voltage _V_ × heating time _t_. - The energy needed to heat the liquid = mass of liquid (mliq) × specific heat capacity of liquid (cliq) × temperature rise (ΔΘ). - The energy needed to heat the calorimeter = (mass of calorimeter (mcal) × specific heat capacity of calorimeter (Ccal) × temperature rise (ΔΘ)). Assuming no heat loss to the surroundings, IVt = mliqliqΔθ + mcalcalΔθ. So, cliq can be calculated from this equation because all of the other quantities are known. ### Continuous Flow Heating In an electric shower, water passes steadily through copper coils heated by an electrical heater. The water is hotter at the outlet than at the inlet. This is an example of continuous flow heating. For mass m of liquid passing through the heater in time t at a steady flow rate, and assuming no energy transfer by heating to the surroundings: - the electrical energy supplied per second _IV_ = _mc_ ΔΘ/t where ΔΘ is the temperature rise of the water and _c_ is its specific heat capacity. Note that when the outflowing water has attained a steady temperature, the temperature of the copper coils does not change, so no mcΔΘ term is needed for the copper coils in the above equation. For a solar heating panel, the energy gained per second by heating the liquid that flows through the panel is equal to mcΔΘ/t. ## 22.3 Change of State When a solid is heated and heated, its temperature increases until it melts. If it is a pure substance, it melts at a well-defined temperature, called its melting point. Once all the solid has melted, continued heating causes the temperature of the liquid to increase until the liquid boils. This occurs at a certain temperature, called the boiling point. The substance turns to a vapour as it boils away. The three physical states of a substance, solid, liquid, and vapour, have different physical properties. For example: - The density of a gas is much less than the density of the same substance in the liquid or the solid state. This is because the molecules of a liquid and of a solid are packed together in contact with each other. In contrast, the molecules of a gas are on average separated from each other by relatively large distances. - Liquids and gases can flow, but solids can't. This is because the atoms in a solid are locked together by strong force bonds, which the atoms are unable to break free from. In a liquid or a gas, the molecules are not locked together. This is because they have too much kinetic energy, and the force bonds are not strong enough to keep the molecules fixed to each other. ### Learning Objectives - Define latent heat. - Measure latent heat. - Explain why the temperature of a substance stays steady when it is changing state. ### Latent Heat When a solid or a liquid is heated so that its temperature increases, its molecules gain kinetic energy. In a solid, the atoms vibrate more about their mean positions. In a liquid, the molecules move about faster, still keeping in contact with each other, but free to move about. 1. When a solid is heated at its melting point, its atoms vibrate so much that they break free from each other. The solid therefore becomes a liquid due to energy being supplied at the melting point. The energy needed to melt a solid at its melting point is called latent heat of fusion. 2. When a liquid is heated at its boiling point, the molecules gain enough kinetic energy to overcome the bonds that hold them close together. The molecules therefore break away from each other to form bubbles of vapour in the liquid. The energy needed to vaporise a liquid is called latent heat of vaporisation. Latent heat is released when a liquid solidifies. This happens because the liquid molecules slow down as the liquid cools until the temperature decreases to the melting point. At the melting point, the molecules move slowly enough for the force bonds to lock the molecules together. Some of the latent heat released keeps the temperature at the melting point until all the liquid has solidified. Latent means hidden. Latent heat supplied to melt a solid may be thought of as hidden because no temperature change takes place even though the solid is being heated. Fusion is a word used for the melting of a solid because the solid fuses into a liquid as it melts. Latent heat is released when a vapour condenses. This happens because the vapour molecules slow down as the vapour is cooled. The molecules move slowly enough for the force bonds to pull the molecules together to form a liquid. Some solids vaporise directly when heated. This process is called sublimation. In general, much more energy is needed to vaporise a substance than to melt it. For example, 2.25 MJ is needed to vaporise 1 kg of water at its boiling point. In comparison, 0.336 MJ is needed to melt 1 kg of ice at its melting point. The energy needed to change the state of unit mass (i.e., 1 kg) of a substance at its melting point (or its boiling point) is called its specific latent heat of fusion (or vaporisation). The specific latent heat of fusion, _l_, of a substance is the energy needed to change the state of unit mass of the substance from solid to liquid without change of temperature. The specific latent heat of vaporisation of a substance is the energy needed to change the state of unit mass of the substance from liquid to vapour without change of temperature. So, the energy _Q_ needed to change the state of mass _m_ of a substance from solid to liquid (or liquid to vapour) without change of temperature is given by Q = ml where _l_ is the specific latent heat of fusion (or the specific latent heat of vaporisation). The unit of specific latent heat is Jkg-1. ## 22.4 Energy Transfer by Heating Energy transfer due to a temperature difference takes place by three main methods which are thermal conduction, convection, and radiation. Evaporation from the surface of a liquid also causes transfer of energy from the liquid. This effect causes a liquid to cool because the faster molecules leave it. Conduction takes place in solids, liquids, and gases. Convection takes place in liquids and gases only. For example, energy from a hot radiator reaches other parts of a room due to thermal conduction through the radiator panel, which heats the air and causes convection currents and also radiates infrared radiation throughout the room. ### Convection When a fluid is heated it becomes less dense and it rises because it is less dense than the cold fluid. In a closed space, the fluid circulates as the hot fluid rises and cold fluid is drawn into the source of heating where it heats up and rises. This process is known as convection. Some examples are listed below. 1. A hot air balloon rises because a gas burner heats the air in the balloon and makes it less dense than the surrounding air. Without repeated bursts of heating, the hot gas in the balloon would cool and the balloon would sink as the air in it becomes more dense. 2. Ocean currents such as the Gulf Stream are convection currents of warm water that flow at or near the ocean surface from hot to colder regions. 3. Hot gases from the flames of a gas fire rise, drawing air into the gas fire. The products of combustion include carbon monoxide, which is lethal if allowed to build up. For this reason, gas fires must be well ventilated so that the products of combustion escape into the atmosphere and fresh air is drawn into the room where the heater is. ### Thermal Conduction Some materials conduct heat much more effectively than others. The thermal conductivities of the rods can thus be compared. - **Metals are better conductors of energy than non-metals** because of the presence of conduction electrons in metals. When a metal is heated, the electrons gain energy and move about faster, transferring energy to atoms and electrons elsewhere. - **Non-metals do not contain conduction electrons and therefore do not conduct as well as metals.** Thermal conduction in a non-metal takes place as a result of vibrations of the atoms spreading throughout the non-metal. Heating a non-metal makes the atoms at the point of heating vibrate more, and these vibrations cause atoms to vibrate in other parts of the non-metal. This process does occur in a metal but much less than energy transfer due to conduction electrons. ### Learning Objectives - Explain what is meant by thermal conduction, convection, and radiation. - Give examples of heat transfer by each method. - Use the equation Q/t = KA ΔΘ/L to solve simple problems on thermal conduction. - Use U-values to compare energy losses. - Use the equation Q/t = UAΔΘ where U = KA/L. ### Radiation Every object emits electromagnetic radiation due to its temperature. This radiation is known as thermal radiation and consists mostly of infrared radiation, although it would include visible radiation if the temperature is sufficiently high. Thermal radiation is absorbed most effectively by matt black surfaces and least effectively by shiny silvered surfaces. A black body is a body that absorbs all the radiation incident on its surface. For example, a small hole in the surface of a hollow object would act as a black body as any radiation entering the hole would be completely absorbed by the surface of the cavity. The Sun and the stars may be considered as black bodies since any radiation incident on them would be absorbed. A surface that is a good absorber of thermal radiation is also a good emitter. The radiation from a black body is referred to as black body radiation. The energy per second radiated from a surface depends on: - The area, _A_, of the surface – the greater the area, the more energy radiated each second - the surface temperature – the hotter an object's surface is, the more energy it radiates per second - the nature of the surface - the surface of a black body radiates more energy per second than any other surface of the same area and at the same temperature. ### U-Values The rate of energy loss from a building in winter can be reduced using different forms of insulation such as insulating the roof and the floors, fitting double-glazed windows, or, if the walls are double-brick walls, filling the gap between the walls with cavity wall insulation. Different forms of insulation can be compared if the U-value of each form of insulation is known. This is the rate of energy transfer per square metre through the insulating material for a temperature difference across it of 1 K (or 1°C). U-values are expressed in watts per square metre per kelvin (or per °C). For example, a typical single-glazed window has a U-value of 4.3 W m-2K-1. For a given area _A_ of insulation which has a temperature difference ΔΘ across its two surfaces, * The rate of energy transfer through the material = UAAθ * where U is the U-value of the insulation. Note that for a single material of thermal conductivity k and thickness L, comparison on the two equations above gives U = k/L ==End of OCR for page 1==