Energy Transfer and Thermodynamics - Math Problem Example

Title: 353472 - Energy Transfer and Thermodynamics Dated: March 18, 2009 1) Define the four laws of thermodynamics using words, diagrams and equations where appropriate. a). Zeroth Law of Thermodynamics which deals with the thermal equilibrium and states, if two Thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other. The law implies that the thermal equilibrium in the Thermodynamic systems is an equivalence relations between the systems as studied under these systems.Methamatical equation for the law is represented with the use of symbols T=Temperatue,and A,B and C are the three systems and the equivalence relation among all these systems is give below: If T(A)= T(B),if T(B)= T(C),Then T(A)= T(C) b). First law of Thermodynamics is about the conservation of energy and states, “The change in the internal energy of a closed system is equal to the sum of the amount of energy supplied in the form of heat and the work done on the system”. Equation: Du= δQ- Δw where δQ is a small amount of heat added to the system,dU is a small increase in the internal energy of the system, and δW is the small amount of work done by the system during the operations of the system. c). The second law of Thermodynamics is about entropy and states that the entropy of an isolated system which is not in equilibrium will tend to increase over time, and approaching to a maximum value at equilibrium. d). The third law of Thermodynamics is a statistical law which states as under: 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) Answer: Entropy is a measure dealing with the disorder of a system. The concept is applied to the systems as studied in Physics, Mathematics and Chemistry regarding the behavior of the molecules during energy changes and transfer of heat during the operations of the systems. When ice melts into water molecules ,the system absorb heat from the surroundings and therefore their motion increases. Entropy increases in this position. 3) Calculate ΔS for the following reaction, using the information in a Table of Thermo chemical 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) Answer: For the equation 2 NO (g) + O2 (g) →N2O4 (g), ΔS= Δq /T where Δq= +155.65 kJ and T = 273, so . ΔS= Δq /T =155.65/273 =0.57 kJ at the temperature absolute zero. Based on the entropy change a spontaneous reaction between the reactants is predicted as the system will react to establish a relationship on the basis of any change in the entropy. 4) These questions test your understanding of temperature measurements and temperature scales. i) What is absolute zero on the Kelivin, Celsius, Fahrenheit and Rankine scales? ii) The boiling point of water if 100°C what is this in Kelvins? iii) The temperature of a system rises by 30°C during a heating process. Express this rise in temperature in Kelvins. iv) The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C. Answer: Absolute zero on the Kelivin scale is determined as [K] = [°C] + 273.15, Absolute zero on the Celsius scale is determined as [°C] = [K] − 273.15, Absolute zero on the Fahrenheit scale is determined as [°F] = [K] × 9⁄5 − 459.67, and Absolute zero on the Rankine scale is determined as [°R] = [K] × 9⁄5 (ii) If the boiling point of water is 100°C, than in Kelvin’s scales = [K] = [100°C] + 273.15= 373.15 (iii) When the temperature of a system rises by 30°C during a heating process, then in Kelvin’s scales the rise =30+273.15=303.15 K iv) The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C, then [°F] = [K] × 9⁄5 − 459.67=60 +459.67*5/9 = 288.7, so [K] =288.7, [°R] = [K] × 9⁄5, [°R] = 288.7× 9⁄5 =519.67, and [K] = [°C] + 273.15, [288.7] = [°C] + 273.15=288.7-273.15= 15.55 5) How is work related to equilibrium? (1 mark) Answer: Work done is positively correlated with the equilibrium and if there is no change in the equilibrium, it means there is no work done by the body. 6) Give examples of equilibrium state, steady state and uniform. Answer: Consider a paratrooper jumping out of a plane a few moments later his parachute opens and he starts falling with uniform velocity. At this stage, the force of gravity acting vertically downwards on the paratrooper is balanced by the reaction of the air in the parachute which acts upward. Thus, the net force on the paratrooper is zero so the paratrooper falls downward with uniform velocity. This is the state of equilibrium. Example of steady state :The amount of hydrogen is continuously created in the universe as the universe expands. At uniform state there is a balance between the reactants and products as shown in the equation: 2 NO (g) + O2 (g) →N2O4 (g) 7) State whether the following are open or closed systems, give reasons for your answer. i) Rechargeable battery, ii) Household refrigerator, iii) Radiator. Answer: .i ) Rechargeable battery is an open system as it requires the external source for its recharging to the optimum level. ii) Household refrigerator is a closed system as it maintains the temperature at the desired level through its normal functioning. iii) Radiator is an open system as it emits radiation to the surroundings and received a source of energy for its normal functioning from the system. 8) What is the difference between a gas, a liquid and a solid? Answer: Solids Liquids Gases Molecules are closely packed. Molecules have small space between them. The intermolecular forces are strong. The intermolecular forces are intermediate between solids and gases. The intermolecular forces are weak. 9) What does thermodynamics tell us with regards to heat transfer? Answer: Thermodynamics tell us that heat energy can be converted into equivalent amount of work, leaving a change in the working system. 10) Explain the difference between internal energy (u) and enthalpy (h). Answer: Internal energy Enthalpy The sum of all the microscopic energies of the molecules of a substance within the object. 11) The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. Answer: Heat release rate is determined with the help of the net result of sum of all the heats formed by the products minus the heat produced by the reactants during a chemical reaction. 12) 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: The law can be stated in two equivalent forms as a0 the integral form and the differential form. Thermal conductivity which is denoted by k, is the property of a material that shows its ability to conduct heat. The mathematical formula for thermal conductivity is as under: (Note: is the temperature gradient) Typical units in SI: W/(m·K). The thermal conductivity of metals is high, for example the thermal conductivity of Aluminum, gold, copper and silver is 200,318,380 and 429, respectively. For hollow fill Fiber insulation the value is 0.042 and for air is 0.025. The negative sign in the Fourier's law indicates the negative gradient in the temperature. 13) 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: The Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body in the unit time is directly proportional to the fourth power of the black body's thermodynamic temperature T which is also called as absolute temperature T. It is a measure of a material's ability to radiate absorbed energy (c)What role does the view factor play in determining the rate of heat transfer? The view factor is the fraction of radiation of the leaving surface A that strikes the surface B. The nature of the leaving surface plays an important role in determining the rate of heat transfer between the bodies of variant heat quantities. (d)What is a blackbody? A black body is a solid block having a hollow cavity with in it. It has a small hole and radiation can enter or escape out through this hole. 14) Explain the Newton’s Law of Cooling. What is the heat transfer coefficient? What is the Nusselt number (10 marks) Answer: The law he following formula: Where Q = Thermal energy in Joules h = heat transfer coefficient A = Surface area of the heat being transferred T0 = Temperature of the object's surface Tenv = Temperature of the environment Where h = heat transfer coefficient, W/ (m2K) A = heat transfer surface area, m2 ΔT = difference in temperature between the solid surface and surrounding fluid area, K Δt = time period, s ΔQ = heat input or heat lost, J There are two major types of convection that is forced convection, in which the heat is carried passively by a fluid motion which can occur anyway without the heating process and natural convection, in which the heat is transported through fluid motion of the molecules and is the type of heat convection which is more complicated than that of the forced convection. 15) 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: The heat of combustion which is denoted by ΔHc0 is the energy released in the form of heat when one mol of a compound undergoes complete combustion process with the use of oxygen. It may be expressed with the following quantities: a) energy/volume of fuel b) energy/mole of fuel (J/mol) and c) energy/mass of fuel The heat release rate is the rate at which the heat as energy is released from the system into the surroundings and is measured in terms of joules per second. For example when a substance is burning with the use of oxygen the energy in the form of heat is released from the system to the surroundings with a net flow of heat. A combustion reaction is a type of chemical reaction that entails oxygen and generates energy in the form of heat so swiftly that a flame is formed. This type of reaction occurs between certain types of compounds like hydrocarbons with oxygen. The product of these types of reactions in the shape of Carbon dioxide and water. The reaction can be illustrated with the help of the following equation: C(x)H(x)+O(2→H2O(g)+CO2(g) There are different types of combustion as rapid, slow, complete, turbulent, micro gravity and incomplete combustions. All of these types are on the basis of the overall combustion process with the use of oxygen. For example eight times the heat energy is required of an ingot of magnesium than that required for lead of the same mass. The symbol of heat capacity is C or c. The equation for latent heat is as under: Q = m L In the equation: Q is the amount of energy released or absorbed during the change of phase of the substance (in joules), m is the mass of the substance, Calorimetry is the phenomenon of measuring the heat of physical changes or chemical reactions. Chemical equilibrium: In a chemical process, it is a state where the chemical activities or concentrations of the product and reactants have no net change over time. Usually, it would be the state that results when the forward chemical process proceeds at the same rate as their reverse reaction. The reaction rates of the forward and reverse reactions are generally not zero but, being equal; with no net changes in any of the reactant or product concentrations. An example of the chemical equilibrium is as under: CH3CO2H + H2O ⇌ CH3CO2− + H3O+ 16) What is the efficiency of an engine that produces 150J of work from 212J of energy? Answer: As efficiency= output (work)/input (energy), so the efficiency of the engine will be 150/212=0.7075, so its efficiency will be 70.75%. 17) 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? Answer: When 100 gram water is added with a temperature of 85°C into a water of 150g with 10°C, then the overall temperature will be 55 °C as the higher temperature will enhance the temperature fro 10°C to upward side as to 55°C. 18) 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. Answer: The initial rate of heat which flow through the Styrofoam is the product of the volume of the material and the surface area and is divided by the temperature as 6*390*550/850=15740. The completion time is 30 .00 minutes. 19) Define flame? Describe the different types of flames and whether they are laminar or turbulent. (2 marks) Answer: Flame is the visible part of a fire which is caused by an exothermic reaction for example through combustion with the utilization of oxygen. There are two different types of flames as diffusion flame in which oxygen and fuel diffuse together in each other, These are laminar type of flames as these also mix with the surrounding oxygen during and after the burning process (1). 20) Define fluid. Answer: A substance that continually deforms (flows) under an applied shear stress is called a fluid. Viscosity of a fluid: It is an opposing force which comes into play when one layer of fluid moves relative to another. The internal friction between two layers of a fluid which stops the relative motion among the layers is called viscosity. 21) Answer: As air is a gas so it can be compressed easily because it has a large space between its molecules and can move from one position to the other. Water can also be compressed but up to some extent as the space between the molecules is not as much as that of gases. 22) Answer: As a result there will be an increase in length although the increase will be negligible. 23) Answer: Distance moved=5m, Force= 30N, Work= (Distance moved) (force), (5)(30)= 150J Energy= mgh, mg=F, h= distance moved, so energy = (F) (distance moved), Energy = (5) (30) = 150N. 24) Answer: There will be an increase in the length of Aluminum as on the basis of an increase in temperature but the increase will be negligible. 25) Define boundary layers. Draw a velocity profile for a fluid in a pipe showing both laminar and turbulent flow. Answer: a boundary is that layer of fluid in the immediate vicinity of a bounding surface for the liquid. It is a phenomenon of viscous forces which relates to the Reynolds number of the liquid. Boundary layers are of different types on the basis of their structures and the circumstances under which these layers are created. All the particles of the liquid does not flow at the same velocity in the pipe, the central particles move at a rapid speed with laminar flow as compare to that particles which face the boundary walls which flow with turbulent flow within the pipe as in the shape of resistance. If the flow is laminar, the velocity distribution at a cross section will be parabolic and in turbulent flow case, the velocity distribution flow will be equal at all the places of the turbulent flow of the boundary layer. Reference: 1. Law, C. K. (2006). "Laminar premixed flames". Combustion physics. Cambridge, England: Cambridge University Press. p. 300. ISBN 0521870526 Read More