[56], MaxwellBoltzmann (MB) occupancy distribution, Energy transformation (Energy conversion), "Reciprocal Relations in Irreversible Processes. Where is this scripture located in the Kings James bible? [40][41][42], The BTE for photon particle momentum pph = phs/uph along direction s experiencing absorption/emission Determine the image distance and image height for a 5.00-cm tall object placed 20.0 cm from a concave mirror having a focal length of 15.0 cm. In this case, the object is located beyond the center of curvature (which would be two focal lengths from the mirror), and the image is located between the center of curvature and the focal point. Thermal energy storage is the concept of heating or cooling a medium to use the energy as per requirement. For the case of optically thick medium of length L, i.e., phL >> 1, and using the gas kinetic theory, the photon conductivity kph is 16SBT3/3ph (SB: StefanBoltzmann constant, ph: average photon absorption), and photon heat capacity nphcv,ph is 16SBT3/uph. . Similar to the body efficiency, the efficiency of any energetic process can be described as the amount of energy converted from the input form to the desired form divided by the original input amount. So the formation of salt releases almost 4 kJ of energy per mole. We have worksheets for the following physics equations: Paper 1: Energy. The use of these diagrams was demonstrated earlier in Lesson 3. From the linear dispersion relation (i.e., dispersionless), phase and group speeds are equal (uph = d ph/d = ph/, uph: photon speed) and the Debye (used for dispersionless photon) density of states is Dph,b,d = ph2dph/2uph3. 3. {\displaystyle {\dot {s}}_{i{\mbox{-}}j}} Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Ch 12. The gravitational mass and an inertial mass appear equal. {\displaystyle \textstyle {\dot {s}}_{f,ph,i}} Unit 5 Lab: Friction Forces and Equilibrium, 105. To apply force, we need to do work. Jacobs ladder of density functional approximations for the exchange-correlation energy. The heat transfer processes (or kinetics) are governed by the rates at which various related physical phenomena occur, such as (for example) the rate of particle collisions in classical mechanics. We will learn more about how temperature and heat transfer are related in the next unit. In physics, the kinetic energy of an object is the energy that it possesses due to its motion. Our goal is to make science relevant and fun for everyone. It does absorb a small amount of thermal energy. The directions of both the displacement and the applied force in the system in Figure 7.3 are parallel, and thus the work done on the system is positive.. We use the letter U to denote electric potential energy, which has units of joules (J). The enthalpy (or latent heat) of melting describes the transition from solid to liquid (the reverse is minus this value and called the enthalpy of fusion), the enthalpy of vaporization describes the transition from liquid to gas (and the opposite is condensation) and the enthalpy of sublimation describes the transition from solid to gas (the reverse is again called the enthalpy of condensation). light-emitting diode, solar photovoltaic cells, etc.). An amount of thermal energy transferred due to a difference in temperature. The Schrdinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. In gas, constant-pressure specific heat capacity cp,f has a larger value and the difference depends on the temperature T, volumetric thermal expansion coefficient and the isothermal compressibility [cp,f cv,f = T2/(f), f: the fluid density]. {\displaystyle \tau _{e}=1/{\dot {\gamma }}_{e}} This phenomenon is generally possible in fluids. Instead, we break down the fat molecules into smaller molecules and then break bonds within those molecules to release chemical potential energy, which we eventually convert to work and exhaust heat. Stay tuned to the. The following diagram summarizes the basic energetic functioning in the human body. The final answer is rounded to the third significant digit. Each equation contains four variables. To accelerate an object, we have to apply force. Relating the thermoelectric coefficients to the microscopic transport equations for je and q, the thermal, electric, and thermoelectric properties are calculated. {\displaystyle e_{f}=(k_{\mathrm {B} }T^{2}/m)(\partial \mathrm {ln} Z_{f}/\partial T)|_{N,V}. where we have defined positive to be pointing away from the origin and r is the distance from the origin. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. The joule (/ d u l / JOOL, also non-standard / d a l / JOWL; [disputed discuss] symbol: J) is the unit of energy in the International System of Units (SI). Optical phonons have higher energies (frequencies), but make smaller contribution to conduction heat transfer, because of their smaller group velocity and occupancy. A magnified, inverted image is located a distance of 32.0 cm from a concave mirror with a focal length of 12.0 cm. The race is not given to the swift but to those that endure to the end. The average temperature between\(94^{\circ} C\)and \(86^{\circ} C\). The specific heat of oil is 2.1 J/Kg C, Temperature difference, \(\Delta T\) = 80C. All bodily functions, from thinking to lifting weights, require energy. Lasers range far-infrared to X-rays/-rays regimes based on the resonant transition (stimulated emission) between electronic energy states. He was also a science blogger for Elements Behavioral Health's blog network for five years. The solution is shown below. One of the most important equations when dealing with internal energy is the first law of thermodynamics, which states that the change in internal energy of a system equals the heat added to the system minus the work done by the system (or, plus the work done on the system). Learn about the conservation of energy at the skate park! Heat engines are still governed by the First Law of Thermodynamics, so any exhaust heat must have been thermal energy that was not used to do work. Geothermal energy: It is obtained from sources like natural geysers, volcanoes, hot water springs, and magma inside the Earths crust. s The most basic way to calculate enthalpy change uses the enthalpy of the products and the reactants. We call the energy that is transferred kinetic energy, and it depends on the mass and speed achieved. In heat transfer physics, the interaction kinetics of phonon is treated using the perturbation theory (the Fermi golden rule) and the interaction Hamiltonian. All matter with a nonzero temperature is composed of Thermal Energy is the total energy of the particles in a material, which is measured as: Change in thermal energy= mass X Change in temperature X specific heat. The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is[6], Once states and kinetics of the energy conversion and thermophysical properties are known, the fate of heat transfer is described by the above equation. Second, our bodies cant just interchange mass and energy they arent the same physical quantity and dont even have the same units. These quantum energy states of the fluid particles are found using their respective quantum Hamiltonian. Your body is capable of releasing the chemical potential energy in your food without combustion, which is good, because you are not capable of using thermal energy your from yourinternal energy to do work. = First, lets calculate the change in gravitational potential energy: The person did work in converting chemical potential energy in their body to mechanical energy, specifically gravitational potential energy. Thermal energy refers to the energy contained within a system that is responsible for its temperature. The following lines represent the solution to the image distance; substitutions and algebraic steps are shown. In the adiabatic steps 2 and 4 of the cycle shown in Figure 4.7. The atoms and smaller molecules that resulting from breaking the bonds combine to form carbon dioxide and water vapor (CO2 and H2O) and we breath them out. the process of burning, the rapid chemical combination of a substance with oxygen, involving the production of heat and light, work done on the external environment, such as moving objects, as apposed to work done internally, such as pumping blood, devices for converting thermal energy to useful work and exhaust heat, ratio of useful work performed to total energy expended, the effectiveness of a machine in transforming the energy input to the device to mechanical energy output, a force that acts on surfaces in opposition to sliding motion between the surfaces, potential energy stored in objects based on their relative position within a gravitational field, unit of energy equivalent to 4.184 Joules, International standard (SI) unit of Energy. Fossil fuels: Thermal energy is released by the burning of fossil fuels. from a hotter body to a colder body). e is determined by electron scattering rates The equation is stated as follows: The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). Photons interact with electric and magnetic entities. Some main uses of thermal energy are listed below. The following table shows the oxygen and corresponding energy consumption rates for various activities. 625 citations 3548 Views. The total energy of the particle is indicated by a cross on the ordinate axis. Atomic orbital, a mathematical function describing the wave-like behavior of either an electron or a pair of electrons in an atom, can be found from the Schrdinger equation with this electron Hamiltonian. To determine the image distance, the mirror equation will have to be used. Again, a negative or positive sign in front of the numerical value for a physical quantity represents information about direction. It helps us to study the characteristics of an open, closed and an isolated system of particles with changes in their temperature. s Integral from initial to final of the internal energy or Check out the energy systems tab in this simulation to visualize different energy conversion systems, energy stored in the chemical bonds of a substance, the total of a systems thermal energy and chemical potential energy, the total energy stored microscopically within the system, energy stored in the microscopic motion of atoms and molecules (microscopic kinetic energy). Unit 7 Lab: Free-Falling and Reaction Time (Distance Learning Compatible). \(\dfrac{change\ in\ temperature}{change \ in \ time} = KT\), \(\dfrac{8^{\circ} C}{2 min} = K(70^{\circ} C)\), The average of\(69^{\circ} C\) and \(71^{\circ} C\) is \(50^{\circ} C\). In 2 mins, when the room temperature is at \(86^{\circ} C\). Sodium chloride (table salt) has an enthalpy of 411 kJ/mol. View the skater's kinetic energy, potential energy, and thermal energy as they move along the track. [39], Near-field radiation from thermally excited dipoles and other electric/magnetic transitions is very effective within a short distance (order of wavelength) from emission sites. Find out the total heat obtained by the system. Build tracks, ramps, and jumps for the skater. produces thermal energy. Because this energy enters or leaves a system during a phase change without causing a temperature change in the system, it Q mC p T. You can calculate changes in enthalpy using the simple formula: H = Hproducts Hreactants. The equation of motion for the lattice vibration in terms of the displacement of atoms [d(jl,t): displacement vector of the j-th atom in the l-th unit cell at time t] is, The phonon dispersion relation gives all possible phonon modes within the Brillouin zone (zone within the primitive cell in reciprocal space), and the phonon density of states Dp (the number density of possible phonon modes). So, heat transfer physics covers the four principal energy carries and their kinetics from classical and quantum mechanical perspectives. Hesss law is useful for when the reaction youre considering has two or more parts and you want to find the overall change in enthalpy. 4. Use 1 / f = 1 / do + 1/di where f =15 cm and do=45 cm, Then use hi / ho = -di / do where ho = 5 cm, do = 45 cm, and di = 60.0 cm. For 5 moles of ice, this is: Now multiply the enthalpy of melting by the number of moles: Calculations for vaporization are the same, except with the vaporization enthalpy in place of the melting one. In the case of the image distance, a negative value always means behind the mirror. For example, electric dipole which in turn are excited by optical phonons or fluid particle vibration, or transition dipole moments of electronic transitions. - To determine the image height, the magnification equation is needed. Athletes have a greater BMR due to this last factor. Instead, the additional thermal energy acts to loosen bonds between molecules or atoms and causes a phase change. The amount of thermal energy. The surface reflectance R of an ideal surface with normal incident from vacuum or air is given as[55] R = [(n - 1)2 + 2]/[(n + 1)2 + 2]. The energy radiated by electromagnetic waves is called radiation. There are many different scales by which you might measure temperature, but the most common ones are the Fahrenheit scale, the Celsius scale and the Kelvin scale. The first law of thermodynamics -> U = q+w where, q is heat and w is work The formula of mechanical energy is M.E = K. E + P.E M.E = mv2 + mgh Where m = mass of an object v = velocity of that object g = acceleration due to gravity h = height of an object. This means that if reaction transforms on substance into another, it doesnt matter if the reaction occurs in one step (reactants become products immediately) or whether it goes through many steps (reactants become intermediaries and then become products), the resulting enthalpy change is the same in both cases. Example 1. Molecules with multiple atoms (nuclei and their electrons) have molecular orbital (MO, a mathematical function for the wave-like behavior of an electron in a molecule), and are obtained from simplified solution techniques such as linear combination of atomic orbitals (LCAO). The molecular orbital is used to predict chemical and physical properties, and the difference between highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is a measure of excitability of the molecules. The enthalpy change of a reaction is the amount of heat absorbed or released as the reaction takes place, if it happens at a constant pressure. Inserting these values gives: H = 411 kJ/mol (239.7 kJ/mol 167.4 kJ/mol), = 411 kJ/mol + 407.1 kJ/mol = 3.9 kJ/mol. The change of the entropy-of-mixing upon adding an electron to a system is the so-called Heikes formula. Use of geysers, where heat is stored in water and hot water can be used anytime according to ones convenience. Alternatively, we could have known right off that the exhaust heat must be 4/5 of the total loss of internal energy, because only 1/5 went into doing useful work. By using this website, you agree to our use of cookies. The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). stored or released as a substance changes state can be calculated using the equation: change in thermal energy = mass specific heat capacity temperature change j Equation 1 $$K = \frac {1} {2}mv^2 $$ where K represents kinetic energy, m is the mass of the moving object, and v is the velocity, or speed, at which the object is moving. To determine the image distance, the mirror equation must be used. The precise definition of enthalpy (H) is the sum of the internal energy (U) plus the product of pressure (P) and volume (V). Heat transfer physics describes and predicts, cv,p, Kp, Rp,b (or conductance Gp,b) and Potential to produce massive amounts of energy, especially for commercial and industrial uses. In this case, the combustion of one mole of carbon has H = 394 kJ/mol (this happens six times in the reaction), the change in enthalpy for the combustion of one mole of hydrogen gas is H = 286 kJ/mol (this happens three times) and the carbon dioxide and water intermediaries become benzene with an enthalpy change of H = +3,267 kJ/mol. The spectral absorption coefficient is then found from ph, = 2 /uph. A pan filled with water cools down from \(94^{\circ} C\) to\(86^{\circ} C\), Calculate the thermal energy required to raise the temperature of 1.5kg of oil from \(10^{\circ}\)to\(90^{\circ}\). It is one of the cleanest sources of energy and renewable energy. e The equations above are really related to the physics of heat flow and energy: thermodynamics. Change in Kinetic energy = 635 0 = 635 J. [34][35] Also, fluid particles can be adsorbed on solid surfaces (physisorption and chemisorption), and the frustrated vibrational modes in adsorbates (fluid particles) is decayed by creating e-h+ pairs or phonons. Rearranging the equation yields a new equation of the form: Speed = Wavelength Frequency. Use of heaters in winter seasons, here the heat energy is stored and transferred through electricity in cold seasons. s Quantum electron energy states for electron are found using the electron quantum Hamiltonian, which is generally composed of kinetic (-22/2me) and potential energy terms (e). Assuming a 20% mechanical efficiency in climbing stairs, how much does your internal energy decrease when a 65 kg person climbs a 15mhigh flight of stairs? This page describes how this can be done for situations involving free fall motion. So, the terms represent energy transport, storage and transformation. Because "thermal" means heat, and heat is used in thermal The Physics Classroom Tutorial presents physics concepts and principles in an easy-to-understand language. heat transferred to the environment rather than being used to do useful work, Energy cannot be created or destroyed, only transferred from one type to another and/or from one object to another, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Since phonon is a boson particle, its occupancy follows the BoseEinstein distribution {fpo = [exp(p/kBT)-1]1, kB: Boltzmann constant}. If you know these quantities, use the following formula to work out the overall change: / Learn the Difference Between Light Microscope and Electron Microscope, Learn Heating Effect of Electric Current and its Applications, Heck Reaction: Definition, Mechanism, Types, Stereoselectivity, & Uses, Wavelength of Light: Learn its Meaning and Values for Visible Spectrum, Improper fractions: Definition, Types, Conversion, Steps and example, Types of Functions: Learn Meaning, Classification, Representation and Examples for Practice, Types of Relations: Meaning, Representation with Examples and More, Tabulation: Meaning, Types, Essential Parts, Advantages, Objectives and Rules, Chain Rule: Definition, Formula, Application and Solved Examples, Conic Sections: Definition and Formulas for Ellipse, Circle, Hyperbola and Parabola with Applications, Equilibrium of Concurrent Forces: Learn its Definition, Types & Coplanar Forces, Learn the Difference between Centroid and Centre of Gravity, Centripetal Acceleration: Learn its Formula, Derivation with Solved Examples, Angular Momentum: Learn its Formula with Examples and Applications, Periodic Motion: Explained with Properties, Examples & Applications, Quantum Numbers & Electronic Configuration, Origin and Evolution of Solar System and Universe, Digital Electronics for Competitive Exams, People Development and Environment for Competitive Exams, Impact of Human Activities on Environment, Environmental Engineering for Competitive Exams. This example is a classic example of convection. Thermal radiation reflects the conversion of thermal energy into electromagnetic energy.Thermal energy is the kinetic energy of random movements of atoms and molecules in matter. [1] Transport properties such as thermal conductivity are calculated from these atomic-level properties using classical and quantum physics. Lets understand the concept of conduction by a basic example. Unit 6 Lab: Elastic Modulus and Ultimate Strength, 109. v = f Energy conversion between electric potential and phonon energy is considered in thermoelectrics such as Peltier cooling and thermoelectric generator. (It isn't -44 cm since the negative sign would only correspond to an upright and virtual image.). Significant content in this chapter was adapted from. ), the complex refractive index m(= n + i , n: refraction index and : extinction index) is found, i.e., m2 = e, = e,r, + i e,c,). However, they are only 20% efficient, which means that only 1/5 of the chemical potential energy they use goes into doing useful work. Generally, a material expands when heated. Get Daily GK & Current Affairs Capsule & PDFs, Sign Up for Free The by-product of ocean thermal energy is fresh water. The largest fraction of energy goes to the liver and spleen, with the brain coming next. Change in the thermal energy changes the states of matter. How much thermal energy does the person transfer to the environment as exhaust heat? The net motion of particles (under gravity or external pressure) gives rise to the convection heat flux qu = fcp,fufT. From the calculations in the second example problem it can be concluded that if a 4.0-cm tall object is placed 8.3 cm from a concave mirror having a focal length of 15.2 cm, then the image will be magnified, upright, 8.8-cm tall and located 18.3 cm behind the mirror. The results of this calculation agree with the principles discussed earlier in this lesson. In older works, power is sometimes called activity. Excess thermal energy can be stored for a very long time by the use of different technologies. Integral from initial to final of the internal energy or The EM wave is governed by the classical Maxwell equations, and the quantization of EM wave is used for phenomena such as the blackbody radiation (in particular to explain the ultraviolet catastrophe). Therefore, we can determine the the actual energy consumed during different activities by measuring oxygen use. Kinematic equations relate the variables of motion to one another. This single temperature will generally change exponentially as time progresses (see below). Interaction rates or energy conversion rates can be evaluated using the Fermi golden rule (from the perturbation theory) with ab initio approach. f Big Blue Interactive's Corner Forum is one of the premiere New York Giants fan-run message boards. Apr 10 2008. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordance with Newton's third law.Most rocket engines use the combustion of reactive chemicals to supply the necessary energy, but non Thermal energy is heat energy. V Net Force (and Acceleration) Ranking Tasks, Trajectory - Horizontally Launched Projectiles, Which One Doesn't Belong? Then use hi / ho = -di / do where ho = 5 cm, do = 45 cm, and di = -30.0 cm The process is similar to burning wood in campfire in the end you have much less massof ash than you did original wood. Suppose a heat engine absorbs heat Q1 from R1 and exhausts heat Q2 to R2 for each complete cycle. B Thus, ke increases with the electrical conductivity e and temperature T, as the WiedemannFranz law presents [ke/(eTe) = (1/3)(kB/ec)2 = 2.44108W-/K2]. Unit 5 Lab: Tipping (Distance Learning Compatible), 113. Thermodynamics deals with the relationship between heat and other forms of energy in a system and thermal energy refers to a quantity of heat energy which is responsible for the temperature of a particular system. where q is heat flux vector, c p (T/t) is temporal change of internal energy ( is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and is the energy conversion to and from thermal energy (i and j are for principal energy carriers). Lets study them in detail. Comparing Work-Energy and Energy Conservation*, 89. You complete the calculation in different ways depending on the specific situation and what information you have available. The total energy conversion rate of a personat restis called thebasal metabolic rate (BMR) and is divided among various systems in the body, as shown the following table: The body is capable of storing chemical potential energy and thermal energy internally. The large N limit of superconformal field theories and supergravity. Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. First, we really we mean lose mass because that is the measure of how much stuff is in our bodies and weight depends on where you are (its different on the moon). 24. Solution 1. So the calculation takes place in a few parts. Of course, during vigorous exercise, the energy consumption of the skeletal muscles and heart increase markedly. The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, r H , for the process.It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book tudes de Dynamique chimique (Studies in Dynamic Chemistry).. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. 1, no heat exchange takes place, so S 2 = S 4 = d Q / T = 0. A quantity representing the capacity of an object or system to do work. This property of a material is called thermal expansion. Also, reach out to the test series available to examine your knowledge regarding related exams. Power is a scalar quantity.. Power is related to other quantities; for example, the power involved in moving a ground vehicle is the product of the The electronic energy is included only if temperature is high enough to ionize or dissociate the fluid particles or to include other electronic transitions. Determine the image distance and the image size. The data in the table is for a 76 kg person climbing 116 stairs per minute. | We dont actually shed the atoms and molecules that make up body tissues like fat by burning them. Hope this article was informative and helpful for your studies and exam preparations. e If you know these quantities, use the following formula to work out the overall change: The addition of a sodium ion to a chloride ion to form sodium chloride is an example of a reaction you can calculate this way. integral from initial to final of the enthalpy. Machines that can use thermal energy to do work, such as a combustion engine, are known as heat engines. Formula for Thermal Energy The generalized formula can be written as, C = E t m T C = specific heat capacity. Electrons interact with other principal energy carriers. If there is 5.00 kg of water in the pot, and the temperature is raised by 80.0 K, what is the specific heat of water? Thermal Energy is the total energy of the particles in a Solids with more than one atom in the smallest unit cell representing the lattice have two types of phonons, i.e., acoustic and optical. Unit 10 Lab: Mechanisms of Heat Transfer, 110. Slack phonon conductivity model mainly considering acoustic phonon scattering (three-phonon interaction) is given as[27][28]. "Thermal energy" or "heat". Next identify the unknown quantities that you wish to solve for. [12][13], At yet larger length scales (mesoscale, involving many mean free paths), the Boltzmann transport equation (BTE) which is based on the classical Hamiltonian-statistical mechanics is applied. The other contribution S,trans is the net energy transferred in moving a carrier divided by qT (q: carrier charge). Example Problem #1 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Unit 10 Practice and Assessment Exercises, 101. We often talk about burning calories in order to lose weight, but what does that really mean scientifically?. A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Conceptual ideas develop logically and sequentially, ultimately leading into the mathematics of the topics. Sign In, Create Your Free Account to Continue Reading, Copyright 2014-2021 Testbook Edu Solutions Pvt. Also, study of interaction with photons is central in optoelectronic applications (i.e. Anything that generates heat Kinetic Energy = 0.5 x Mass x (Speed)2) Elastic Potential Energy = 0.5 x Spring Constant x (Extension)2. Ray diagrams can be used to determine the image location, size, orientation and type of image formed of objects when placed at a given location in front of a concave mirror. For many calculations, Hesss law is the key piece of information you need to use, but if you know the enthalpy of the products and the reactants, the calculation is much simpler. = May disrupt the natural aquatic environment by high chances of change in salinity of the water. Gravitational Potential Energy = Mass x Gravitational Field Strength x Height. The occupation has equilibrium distributions (the known boson, fermion, and MaxwellBoltzmann particles) and transport of energy (heat) is due to nonequilibrium (cause by a driving force or potential). See Answer - In a homogeneous system divided into two halves, all its extensive properties, in particular its volume and its mass, are divided into two halves. This falls into the category of Case 5: The object is located in front of F. The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: Like many mathematical problems in physics, the skill is only acquired through much personal practice. The thermal energy conversion rate involving phonon is included in The amount of thermal energy exchanged due to temperature differences is often called heat (). In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. The cost of setting up the ocean thermal energy equipment is expensive. What is the essence of making a thin smear. The internal combustion engines that power most cars operate in similar fashion by converting chemical potential energy in fuel to thermal energy via combustion, then converting some of the thermal energy into useful work and dumping some into exhaust heat. The numerical values in the solution above were rounded when written down, yet un-rounded numbers were used in all calculations. Note also that the image height is a positive value, meaning an upright image. 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