Thermodynamics Assessment - Assignment Example

Thermodynamics Assessment By (Name) (Tutor’s Name) (Course) (University) (Address of College) (Date) 1) Define the four laws of thermodynamics using words, diagrams, and equations where appropriate. (8 Marks) Zeroth Law The law states that a thermodynamic equilibrium is an equivalence relation. It postulates that when two systems have thermal equilibrium with a common third system then the two thermodynamic systems are in thermal equilibrium with one another. Therefore, it means that if system A and B are in thermal equilibrium with C, then Systems A and B are also in thermal equilibrium (Rao 2001: 44). First Law of Thermodynamics The first law of thermodynamics is also known as the law of conservation of energy. The law says that the heat energy supplied in to closed system will be used to do work and increase its internal energy (McCarthy 2005: 16). Therefore, the change in internal energy is given by heat supplied into a closed system minus the work done by that system. Also stated as: Where,  Second Law of Thermodynamics The second law of thermodynamics attempts to overcome the limitations of the first law. It takes into consideration equilibrium states of systems and the processes that link these states with others. It states: “Among all the allowed states of a system with specific values of energy, constraints, and numbers of particles, one and only one is a stable equilibrium state.” The total entropy of an isolated system increases over time towards attaining a maximum value. It indicate that although the net work done is equal to net heat supplied in a cycle, the total heat supplied must be greater than the net work done. The diagram above represents a heat engine in a complete cycle. According to the first law;  From the second law;  According to the second law, thermal efficiency is always less than 100%. Third Law of Thermodynamics This law puts the absolute zero temperature into consideration. It states that the processes will virtually cease when the system asymptotically approaches zero while entropy asymptotically move towards a minimum value. 2) 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) Entropy is a thermodynamic property, which the degree of disorder of molecules in a system. Entropy is directly proportional to the degree of disorder in a system. When ice melts in to water, its molecules get more energy and thus they freely move within the volume. The energy contained in the molecules of water is higher than that of ice. This means that they are more disorderly than in solid state. In such a case therefore, entropy is high. 3) Predict whether entropy will be 0 for the following processes: a. Dry ice melts, Entropy>0 b. Water freezes, Entropy0 4) Calculate ΔS for the following reaction, using the thermodynamic data provided (6 Marks). a. 2NO (g) +O2 (g) → N2O4 (g) b. 3H2 (g) + N2 (g) → 2NH3 (g) c. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l) 5) These questions test your understanding of temperature measurements and temperature scales. a. Body temperature is 37°C what is this in Kelvin, Fahrenheit, and Rankine scales. 37°C = 37+273= 310K 37°C= 98.6°F 37°C = 558.27°Rankine b. What is absolute zero in Celsius, Fahrenheit and Rankine scales? Absolute Zero= -273°C Absolute Zero=459.67°F Absolute Zero=0°Rankine c. The temperature of a system rises by 35°C during a heating process. Express this rise in temperature in Kelvin. Let the original temperature be x°C Final temperature=(x+35) °C, Converting these temperatures to Kelvin; x°C= (x+273) K (x+35) °C=(x+35+273) =(x+308) K Change in Temperature= (x+308)-(x+273) =35K d. The temperature of a system rises by 80°F during a heating process. Express this rise in temperature in R, K, and °C. Rise in temperature in R Rise in temperature in K Rise in temperature in °C  6) The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. (1 Mark) 7) What is Fourier’s Law? Mathematically express Fourier’s Law defining all the terms used within it. 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) Fourier’s Law is equation used to determine the conduction heat flux based on the temperature distribution on a medium. It gives the rate of heat transfer through conduction. Given by: Where Qcond. = The rate of heat transfer through conduction kt=thermal conductivity of the material A=cross-sectional area perpendicular to heat transfer direction dT/dx =temperature gradient in the direction of heat transfer Thermal conductivity kt is the ability of material to conduct heat. This value depends on the arrangement of molecules and availability of free electrons. Metals have higher value of thermal conductivity than insulating materials and gas because they have unattached electron. Fourier’s Law has a negative sign because it is conventionally agreed that the rate of heat transfer is calculated from source’s point of view. It represents heat flowing away from a material. However, if it is approached from sink’s point of view, then the sign must be changed to represent gain of heat. 8) Explain the Stefen-Boltzmann Law. What is emissivity? What are the ranges of values for the emissivity of a surface? Define the terms “black surface” and “grey surface.” What role does the view factor play in determining the rate of heat transfer? What is a blackbody? (10 Marks) Stefen-Boltzmann Law describes the rate of heat transfer from one object to the other through radiation. The two objects must be seeing one another for radiation to take place. The law describes heat transfer through radiation between two objects located in an emitting and non-absorbing medium. The law is given by: Where Qrad=Rate of heat transfer through radiation F1-2=view factor between the two objects/ how well object 1 views object 2 ℰ=dimensionless absorptivity or emissivity of object 1(colder object absorbs while hotter one emits) A1=surface area of object 1 σ= Stefen-Boltzmann constant (5.69 X 10-8 W/m2 or 0.1714X10-8 Btu/h.ft2.R4) T1=Surface temperature of object 1 T2=Surface temperature of object 2 Emissivity, ℰ is the tendency of an object to emit heat through radiation. It ranges from 0 to 1. A material with emissivity of 0 means that it does not emit heat while 1 means that the material completely emits heat. However, these values are just theoretical. A black surface is the one whose emissivity is equal to one, i.e. ℰ=1. On the other hand, a grey surface does not emit or absorb the entire radiation flux. Instead, it radiates a portion according to emissivity, ℰ. View factor, F1-2 shows how well object 1 sees object 2. It gives the proportion of radiations leaving the surface of object 1 and striking the surface of object 2. An idealized body whose surface absorbs the entire incident electromagnetic radiation is classified as a black body. 9) 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) Heat of combustion is the amount of energy released in form of heat when a substance is undergoes combustion in presence of excess oxygen. Combustion reaction occurs when a compound combines with oxygen to produce water, heat, and carbon dioxide (Moran 1999: 2-63). A simple combustion reaction is that of methane: CH4+O2 CO2+H2O+Heat Heat release rate is the speed at which a substance is converted into heat energy in presence of oxygen and high temperatures. Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by 1 degree Celsius. Latent heat is the amount of heat energy released or absorbed by a substance in the process of transformation from one phase to another. Calorimetry is the scientific study of the amount of heat energy changes accompanying chemical reactions. Combustion temperature is the amount of heat at which the entire or part of a substance is converted in to heat, water, and carbon dioxide in presence of oxygen. Chemical equilibrium is a state whereby there is no further chemical reaction in a mixture (Beiser 1988: 60). 10) Determine the rate of heat transfer per unit area for a blackbody at 20°C. Is a good absorber of radiation a good emitter or a poor emitter? (2 Mark) For a black body, emissivity, ℰ=1 11) Does heat depend on the mass of a substance? Does temperature depend on the amount of a substance? (2 Marks) Heat is a measure of amount of energy stored in molecules of a substance and depends on the mass of the substance. Temperature is a measure of concentration of heat. Therefore, it depends on amount of substance. 12) How is natural convection different from forced convection? (2 Marks) Natural convection results from the difference in density due to temperature variations in the fluid. Upon heating, the density is altered along boundary layer making the fluid to be continuously replaced by denser and cooler fluid. Forced convection is the flow of fluid induced by an external force like a fan, pump, or mixer (Pitts and Sissom 1997: 221). 13) Aluminum has a specific heat of 0.902 J/goC. How much heat is lost when a piece of aluminum with a mass of 23.984 g cools from a temperature of 415.0oC to a temperature of 22.0oC? (2 Marks) m=23.984g c=0.902 J/goC Change in temperature= (688-295) =393K 14) A heat engine draws heat from a combustion chamber at 300°C and exhausts to atmosphere at 10°C. What is the maximum thermal efficiency that could be achieved? (2 Marks) 15) The temperature of a sample of water increases by 69.5oC when 24 500 J are applied. The specific heat of liquid water is 4.18 J/goC. What is the mass of the sample of water? (2 Marks) Q=24500J, c=4.18 J/goC and Change in Temperature=69.5K 16) How much energy does it take to raise the temperature of 70 g of copper by 30 °C? Specific heat of copper is 0.385 J/g ºC. (2 Marks) m=70g, c=0.385 J/g oC, Change in Temperature=30K 17) Define the following terms: (2 Marks) a. Heat capacity Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius. b. Specific heat Specific heat is the amount of heat required to raise the temperature of unit mass of a substance by one degree Celsius. 18) Heat is added to a system, and the system does 26 J of work. If the internal energy increases by 7J, how much heat was added to the system? (2 Marks)  19) A 60kg block of iron is heated from 22°C to 152°C. How much heat had to be transferred to the iron? (2 Marks) m=60 Kg, specific heat of heat, c=0.45 J/goC and Change in Temperature=130K 20) 180J of heat are injected into a heat engine, causing it to do work. The engine then exhausts 40J of heat into a cool reservoir. What is the efficiency of the engine? (2 Marks) 21) What is kinetic energy and how does it relate to the temperature of a system? (2 Marks) Kinetic energy is the energy possesses by a body in motion. According to kinetic theory of gases, this energy is directly proportional to absolute temperature of the gaseous substance. Given as: Where k is the Boltzmann’s constant=1.38 X 10-23 J/K 22) 61.6 ml of milk at 18.6°C are added to 455.5 ml of coffee at 90.2°C. What is the final temperature in degrees Celsius of this liquid mixture when thermal equilibrium is reached? Assume coffee has the same properties as pure water. The average density of milk is 1032 kg/m3. The specific heat of milk is 1.97 J/g °C. (2 Marks) Heat gained by milk=Heat lost by coffee Mass of milk in grams: Let T be the final temperature of the mixture Equating the two and solving for T: 23) 1.5kg of cold water at 4°C is added to a container of 1.5kg of hot water at 65°C. What is the final temperature of the water when it arrives at thermal equilibrium? (2 Marks) At equilibrium, Heat gained = Heat Loss 24) Gold has a specific heat of 0.129 J/g °C. If 5.00 g of gold absorbs 1.33 J of heat, what is the change in temperature of the gold? (2 Marks) 25) A gas absorbs 2.5J of heat and then performs 1.5J of work. What is the change in internal energy of the gas? (2 Marks) According to the First law of thermodynamics; 26) Explain the ideal gas law, give the mathematical equation, and define all the terms used. (2 Marks) Ideal gas law is the representation of gas behavior under hypothetical conditions of temperature, volume, and pressure. It is given by: Where P1, V1, and T1 are the pressure, volume, and temperature of the gas at state 1 respectively while P2, V2, and T2 are pressure, volume and temperature of the gas at state 2 (Ramsden 2000: 153) . 27) Explain what intensive and extensive properties are, giving examples of each to support your answer. (1 Mark) Intensive properties are the features, which do not depend on the amount of substance available. Examples: boiling point, color, density, melting point and solubility Extensive properties are those whose values are determined by the amount of substance present. Examples: volume, mass, and weight. 28) Explain Newton’s Law of cooling and give the mathematical equation defining all the terms used. (2 Marks) Heat transfer will occur when the temperature of the object is higher or lower than that of the surrounding fluid. Newton’s law of cooling explains the loss of heat through convection. It is given by:  Where  The algebraic sign of Newton’s law of cooling is conventionally accepted to be positive for situations where T∞>Ts. 29) Discuss the different types of systems encountered in thermodynamics. (3 Marks) Isolated system-this is a system which exchanges neither energy nor matter with the exterior. They do not exist in real life situations Closed system-the interaction with the exterior is restricted to exchange of energy only. This is a system, which can be simulated in the laboratories. Open system-this is a system where there is an exchange of both natter and energy. 30) Discuss the variables that are used to quantify a gas. (2 Marks) Gas is quantified using the following variables: Pressure- this is the amount of force exerted on a surface per unit area Temperature-the measure of heat contained in the gas Volume-The amount of gas present References Beiser, A 1988, Schaum’s Outline of Theory and Problems of Physical Science, McGraw-Hill Companies, Inc., New York McCarthy, R 2005, The Laws of Thermodynamics: Understanding Heat and Energy Transfers, The Rosen Publishing Group, Inc., New York Moran, MJ 1999, Engineering Thermodynamics, CRC Press LLC, Boca Raton Pitts, DR & Sissom, LE 1997, Schaum’s Outline of Theory and Problems of Heat Transfer, McGraw-Hill Companies, Incorporation, New York. Ramsden, EN 2000, A-level Chemistry, Nelson Thornes Limited, London Rao, YVC 2001, Thermodynamics, Universities Press (India) Limited, New Delhi Read More