Energy Transfer and Thermodynamics - Assignment Example

Assessing Learning Outcomes 1, 2, 4 Demonstrate an understanding of the first and second laws of thermodynamics and their applications. Appraise the elementary concepts in combustion: types of combustion, heat of combustion, combustion temperature and chemical equilibrium. 4. Demonstrate an understanding of the behaviour and properties of external flows. INSTRUCTIONS: Please answer all 25 questions, showing workings out where appropriate. Define the four laws of thermodynamics using words, diagrams and equations where appropriate. (8 marks) Answer: Zeroth Law of Thermodynamics – “If object A is in thermal equilibrium with object B, and if object B is in thermal equilibrium with object C, then object A and object C are in thermal equilibrium with each other.” First Law of Thermodynamics - “The change in the internal energy of the system is equal to the difference of the heat transfer into the system and the work done by the system.” In mathematical terms, E = Q - W where E is the internal energy of the system, Q is the heat transferred into the system, and W is work done by the system. Second Law of Thermodynamics - “Energy naturally flows from a region of higher concentration to a region of lower concentration.” It introduces the concept of entropy or randomness which suggests that work does not only depend on the initial and final points but on the process which work is done. This is represented by the equation S>0. . Third Law of Thermodynamics - “All processes stops and the entropy of the system reaches minimum as the system approaches absolute zero”. This means that it is impossible for any system to arrive absolute zero using finite operations. What is entropy? Explain what happens to the motion of water molecules when ice melts into water? What happens to the entropy in this situation? (2 marks) Answer: Entropy is the measure of the randomness or disorder of the system. The more random the system is, the greater the entropy becomes. Molecules of solids have smaller values of entropy compared to the molecules of water because the molecules of water behave in a more random fashion compared to the molecules of solids. In the same manner, the molecules of an ice has smaller value of entropy. When ice melts, the motion of the water molecules increases which in turn increases the entropy of the system. Calculate ΔS for the following reaction, using the information in a Table of Thermochemical Data, and state whether entropy increases (becomes more random) or decreases (becomes less random)? Based on entropy changes, do you predict a spontaneous reaction? 2 NO(g) + O2(g) →N2O4(g) (6 marks) Answer: Given that the entropy for NO(g) = 210.76J/Kmol, O2(g) = 29.378J/Kmol, N2O4(g) = 150.38J/Kmol, the change in the entropy of the reaction is 2(210.76) + 29.378 → 150.38 450.898 → 150.38 The resulting reaction decreases the entropy which means that the product is achieved through stable reactions rather than spontaneous reactions. These questions test your understanding of temperature measurements and temperature scales. What is absolute zero on the Kelivin, Celsius, Fahrenheit and Rankine scales? The boiling point of water if 100°C what is this in Kelvins? The temperature of a system rises by 30°C during a heating process. Express this rise in temperature in Kelvins. The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C. (4 marks) Answer oK oC oF oR Absolute zero 0 -273 -459.67 0 Boiling point 373.15 100 212 671.4 30OC 300.15 60OF 288.70 15.55 519.67 How is work related to equilibrium? (1 mark) Answer: If heat is applied into the system, the system must apply work in order to maintain the equilibrium of its internal energy. From the first law of motion, W = Q - E which details the relationship of work and equilibrium. Give examples of equilibrium state, steady state and uniform. (3 marks) Answer: An equilibrium state is the state where two systems with different properties find a common point of reference which is the equilibrium. An example of systems in thermal equilibrium state is when two objects having different temperatures made contact with each other. The temperature will eventually reach equilibrium. Steady state occurs when minor changes in the system occur but the system as a whole does not vary. An example of a steady state system is a container that dispenses its contents at the same rate its contents is being replaced. The system changes but the system as a whole did not vary. A uniform state is a permanent and constant state. An example of a uniform state is a stationary object in a vacuum. State whether the following are open or closed systems, give reasons for your answer. Rechargeable battery, Household refrigerator, Radiator. (6 marks) Answer: A closed system is a system that draws from its own limited supply of energy. It is also characterized by its ability to exchange heat and work (but not matter) to its environment. A rechargeable battery can be considered as a closed system because it utilizes its own stored energy. In contrast, an open system is a system that utilizes energy from a source with an infinite amount of energy. Refrigerators and radiators are open systems because they draw energy from an external source in order to operate. A rechargeable battery becomes an open system once it is charging. What is the difference between a gas, a liquid and a solid? (2 marks) Answer: In the simplest sense, the difference between a solid from a liquid, a liquid from a gas, and a solid from a gas is the arrangement of the atoms and molecules. The atoms in solids are bounded to each other and its motions are constrained. The atoms in liquids on the other hand have weaker bonding than solids, allowing it to flow freely. Gas molecules can move freely because of the weaker attractions between atoms and molecules. What does thermodynamics tell us with regards to heat transfer? (1 mark) Answer: According to the second law of thermodynamics, heat moves from a region of higher concentration to a region of lower concentration. There are three ways to transfer heat – conduction (or the transfer of heat when bodies are in contact), convection (the transfer or heat through air movement), and radiation (the transfer of heat in vacuum). Explain the difference between internal energy (u) and enthalpy (h). (1 mark) Answer: Enthalpy measures the sum of the internal energies of a system as well as the pressure of the gas and its confining volume. The internal energy on the other hand measures the potential energy of the system as well as its kinetic energy. In other words, enthalpy is a bigger scale compared to internal energy. The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. (2 marks) Answer: HRR = (4 kg/s) (46,,450 kJ/kg) = 185, 800 kJ/s What is Fourier’s Law? What is thermal conductivity? Compare the values of thermal conductivity of metals, insulating materials and gases. What does Fourier's law have a minus sign? (10 marks) Answer: According to Fourier’s Law, the transfer of heat through a material is directly proportional to the negative gradient of the temperature to the area perpendicular to where the heat flows. A negative sign is used in Fourier’s Law to indicate that the direction of the heat transfer is opposite the direction of the area with the greatest rate of heat transfer. A concept associated with Fourier’s Law is thermal conductivity which is a property of materials to conduct heat. Air in vacuum is a good insulator and has low values for conductivity. Insulators also have low values for conductivity. Metals are good conductors and so has typically large conductivity values. Air has a thermal conductivity of 0.025W/mK whereas lead has 35.3W/mK. Explain the Stefen-Boltzman Law. What is emissivity? What role does the view factor play in determining the rate of heat transfer? What is a blackbody? (10 marks) Answer: Stefen-Boltzman Law states that the total energy radiated on the surface area of a blackbody is proportional to the thermodynamic temperature of the blackbody. In equation form, J = σT4. Stefan-Boltzman Law introduces emissivity which is the ratio of the energy radiated by a material to the energy radiated by a blackbody given the same temperature. A blackbody is a theoretical cavity that absorbs (or traps) all types of radiation incident to it. When heated, blackbodies emit radiation of the same spectrum. View factor measures the proportion of the radiation leaving one surface to the radiation that hits the surface. The greater the influx of radiation that hits the surface of another body, the greater amount of heat is conducted to the surface. Explain the Newton’s Law of Cooling. What is the heat transfer coefficient? What is the Nusselt number? What are the two types of convection? (10 marks) Answer: Newton’s Law of Cooling defines the rate of heat loss experienced by a body which is proportional to the difference in temperatures between the body and its surroundings. Through Newton’s Law of Cooling, heat transfer coefficient is measured and calculated. Heat transfer coefficient is the rate with which heat is transferred from solid to liquid or from liquid to solid. Heat transfer occurring on the boundary layers introduces the Nusselt number which is a dimensionless number that indicates the ratio of convective and conductive heat transfer that occurs on boundary layers. There are two types of convection which are natural convection wherein heating causes the fluids to move and forced convection where the fluid moves without being heated. Define heat of combustion, heat release rate and combustion reaction giving appropriate equations. Explain the different types of combustion and definitions of the following: Specific heat capacity, latent heat, calorimetry, combustion temperature and chemical equilibrium. (10 marks) Answer: Heat of combustion – the amount of energy released in the form of heat when a unit of a compound undergoes combustion with oxygen. It is expressed in the following equation co = Ecomb + VP Heat release rate – is the rate of heat release during combustion. It is defined by the equation Q = comA. Combustion reaction – a rapid chemical reaction that involves oxygen to produce energy in the form of heat resulting to a flame. One form of this equation is C(x)H(x)+O(2)→H2O(g)+CO2(g) Types of combustion 1. rapid combustion – a combustion where large quantities of light and heat energies are formed durng the brief intervals of combustion. 2. slow combustion - combustions that typically occur at low temperatures like cellular level combustions. 3. complete combustion – the fuel consumes all oxygen present in the reaction. 4. incomplete combustion – combustion where there is insufficient oxygen in the reaction and water and carbon dioxide appears as by products. 5. turbulent combustion – combustions that produce turbulence. 6. microgravity combustion – combustions that occur in vacuum or in space. Specific heat capacity – the amount of heat energy required to increase the temperature to one degree. Latent heat – the amount of energy absorbed by a substance when it undergoes phase change. Calorimetry – the scientific approach of measuring the heat of chemical reactions and physical changes. Combustion temperature – the temperature of the system that undergoes combustion. Chemical equilibrium – the state of chemical reactions when there is no net-change in the chemical property of the reacting substances. What is the efficiency of an engine that produces 150J of work from 212J of energy? (1 mark) Answer:  = 212J/150J = 1.413 A Styrofoam cup (of negligible heat capacity) contains 150g of water at 10°C. If you add 100g of water at a temperature of 85°C what is the final temperature of the mixture after it has been thoroughly mixed? (2 marks) Answer: Qwater = - Qwater (0.15)(T- 10) = - (0.10)(85 – T) 0.25T = 10 T = 40 A closed Styrofoam cup, which is 6 mm thick and has a surface area of 390 cm2, contains 550 ml of hot coffee at 850C. The air outside the cup remains at a constant temperature of 210C. Assuming that the coffee has a mass of 0.6 kg, and that the specific heat capacity is the same as that of water, determine (i) The initial rate of heat flow through the Styrofoam (in SI units), (ii) And the time required for the coffee to cool from 850C to 700C. (6 marks) Answer: (i) Q/t = (10)(0.039)(85 – 21) = 24.96W/s (ii) t = 24.96W/(10)(0.039)(85 –70) = 24.96/57.7 = 0.4s Define flame? Describe the different types of flames and whether they are laminar or turbulent.? (2 marks) Answer: Flames result in the occurrence of combustions and oxidations. Turbulent flames are characterized by chaotic motion and random patterns whereas laminar flames are typically smooth and moves fluidly. Define fluid. What is the viscosity of a fluid? (2 mark) Answer: Fluids are substances that deforms when shear and stress are applied to it. The characteristic of fluids to resist deformity is called viscosity. Is air a compressible fluid or an incompressible fluid? How about water? Explain your answer. (2 marks) Answer: Compressible fluids are fluids that return to their original density when compressed or compacted. Water is an incompressible fluid while air is both compressible and incompressible. A concrete slab has a length of 24 m at -8 ºC on a winter's day. What is the change in length from winter to summer, when the temperature is 35 ºC? The linear expansion coefficient of concrete is 1 X 10-5 ºC-1. (1 mark) Answer: L = 24(1x 10-5)(35+8) = 0.01 m. A box is pushed 5m across a room with a force of 30N. What is the work done and how much energy is used? (1 mark) Answer: W = Fd = (30)(5) = 150J A piece of aluminium siding is 12.45 meters long on a cold winter's day, -18°C. How much longer is it on a very hot summer's day, 37°C? (1 mark) Answer: L = 12.45(2.4x 10-5)(37+18) = 0.016 m. Define boundary layers. Draw a velocity profile for a fluid in a pipe showing both laminar and turbulent flow. (6 marks) Answer: Boundary layers are the layers of the fluid that is present in the surface of the fluid. References Louis C. Burmeister, (1993) “Convective Heat Transfer”, 2nd ed. Publisher Wiley-Interscience. Potter, M. & Scott, E. (2003). Thermal Sciences: An Introduction to Thermodynamics, Fluid Mechanics, and Heat Transfer. New York: Thomson-Engineering. Read More

378 → 150.38 450.898 → 150.38 The resulting reaction decreases the entropy which means that the product is achieved through stable reactions rather than spontaneous reactions. These questions test your understanding of temperature measurements and temperature scales. What is absolute zero on the Kelivin, Celsius, Fahrenheit and Rankine scales? The boiling point of water if 100°C what is this in Kelvins? The temperature of a system rises by 30°C during a heating process. Express this rise in temperature in Kelvins.

The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C. (4 marks) Answer oK oC oF oR Absolute zero 0 -273 -459.67 0 Boiling point 373.15 100 212 671.4 30OC 300.15 60OF 288.70 15.55 519.67 How is work related to equilibrium? (1 mark) Answer: If heat is applied into the system, the system must apply work in order to maintain the equilibrium of its internal energy. From the first law of motion, W = Q - E which details the relationship of work and equilibrium.

Give examples of equilibrium state, steady state and uniform. (3 marks) Answer: An equilibrium state is the state where two systems with different properties find a common point of reference which is the equilibrium. An example of systems in thermal equilibrium state is when two objects having different temperatures made contact with each other. The temperature will eventually reach equilibrium. Steady state occurs when minor changes in the system occur but the system as a whole does not vary.

An example of a steady state system is a container that dispenses its contents at the same rate its contents is being replaced. The system changes but the system as a whole did not vary. A uniform state is a permanent and constant state. An example of a uniform state is a stationary object in a vacuum. State whether the following are open or closed systems, give reasons for your answer. Rechargeable battery, Household refrigerator, Radiator. (6 marks) Answer: A closed system is a system that draws from its own limited supply of energy.

It is also characterized by its ability to exchange heat and work (but not matter) to its environment. A rechargeable battery can be considered as a closed system because it utilizes its own stored energy. In contrast, an open system is a system that utilizes energy from a source with an infinite amount of energy. Refrigerators and radiators are open systems because they draw energy from an external source in order to operate. A rechargeable battery becomes an open system once it is charging.

What is the difference between a gas, a liquid and a solid? (2 marks) Answer: In the simplest sense, the difference between a solid from a liquid, a liquid from a gas, and a solid from a gas is the arrangement of the atoms and molecules. The atoms in solids are bounded to each other and its motions are constrained. The atoms in liquids on the other hand have weaker bonding than solids, allowing it to flow freely. Gas molecules can move freely because of the weaker attractions between atoms and molecules.

What does thermodynamics tell us with regards to heat transfer? (1 mark) Answer: According to the second law of thermodynamics, heat moves from a region of higher concentration to a region of lower concentration. There are three ways to transfer heat – conduction (or the transfer of heat when bodies are in contact), convection (the transfer or heat through air movement), and radiation (the transfer of heat in vacuum). Explain the difference between internal energy (u) and enthalpy (h). (1 mark) Answer: Enthalpy measures the sum of the internal energies of a system as well as the pressure of the gas and its confining volume.

The internal energy on the other hand measures the potential energy of the system as well as its kinetic energy. In other words, enthalpy is a bigger scale compared to internal energy. The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg.

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