Energy Transfer and Thermodynamics - Essay Example

FV1201 Energy Transfer and Thermodynamics. Assignment 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) The Zeroth Law of Thermodynamics is an extension of the principle of thermal equilibrium. It states that two systems in thermal equilibrium with a third system are in equilibrium with each other. In other words, if T1, T2, and T3 are the temperatures of three systems, with T1 = T3 and T2 = T3, then T1 = T2. The First Law of Thermodynamics is often referred to as the Law of Conservation of Energy; energy cannot be created or destroyed. Mathematically, the First Law can be written as: Different processes involving energy changes can occur in the universe, but their sum must be zero. That is, where the ΔUs are the changes in internal energy for the various processes. The First Law predicts that energy added to or removed from a system must be accounted for by a change in the internal energy Δ U. Energy is added to or removed from a system as work, w or heat, q, in which case ΔU = q + w. The Second Law of Thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. The second law expressed in terms of an entropy change is given as: ΔS ≥ 0 (universe). The universe is the pre-eminent example of an adiabatic process. That is, heat cannot flow in or out of the universe. The Third Law of Thermodynamics states that: Every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of a perfect crystalline substance. In a perfectly ordered crystal, every atom is in its proper place in the crystal lattice. At T= 0 Kelvin, all molecules are in their lowest energy state. Such a configuration would have perfect order; and since entropy is a measure of the disorder in a system, perfect order would result in an entropy of zero. Thus, the Third Law gives us an absolute reference point and enables us to assign values to S and not just to ΔS as we have been restricted to do with U, H, A, and G. According to the Third Law, SO=0 thus: 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) The thermodynamic function, ENTROPY, is a state function (like enthalpy and internal energy), which may be thought of as a measure of disorder or randomness. The molecules of water that make up an ice crystal are held rigidly in place in the crystal lattice. When ice melts, the water molecules are free to move about with respect to one another and to tumble around. Thus, in liquid water the individual water molecules are more randomly distributed than in the solid. The well-ordered solid structure is replaced by the much more disordered liquid structure. Thus, the entropy in this situation has increased. 3) 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) A reaction that leads to a decrease in the number of gaseous molecules generally leads to a DECREASE in entropy. The entropy change of this reaction is NEGATIVE because the three molecules of gas react to form one molecule of gas. Processes in which the disorder of the system increases tend to occur spontaneously. I believe this is NOT a spontaneous reaction because of its negative entropy. 4) These questions test your understanding of temperature measurements and temperature scales. (4 marks) i) What is absolute zero on the Kelivin, Celsius, Fahrenheit and Rankine scales? 0 K on the Kelvin scale −273.15° on the Celsius scale Precisely equivalent to 0 °R on the Rankine scale −459.67° on the Fahrenheit scale ii) The boiling point of water if 100°C what is this in Kelvins? [K] = [°C] + 273.15 = 373.15K iii) The temperature of a system rises by 30°C during a heating process. Express this rise in temperature in Kelvins. [K] = [°C] + 273.15 = 303.15K iv) The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C. [°R] = [°F] + 459.67 = 519.67°R [K] = ([°F] + 459.67) × 5⁄9 = 288.71K [°C] = ([°F] − 32) × 5⁄9 = 15.56°C 5) How is work related to equilibrium? (1 mark) In a Carnot cycle a system, as cylinder of gas, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted. Thus, in the process of returning to its equilibrium state, the system may perform work on its surroundings. 6) Give examples of equilibrium state, steady state and uniform. (3 marks) Equilibrium State: A system of interacting particles that is left undisturbed by outside influences. By interacting, they will share energy/momentum among themselves and reach the state where the global statistics are unchanging in time. : A chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components’ Gibbs free energy and a maximum of their entropy Steady State: The thrust of an aircraft engine is not always truly in steady state (because it changes from take-off to cruise), but the transient terms in the energy and mass balances (dECV/dt and dMCV/dt, respectively) are usually small enough compared to the other terms that they may be neglected. Thus the system is treated as a steady state one. Uniform: A flow through a pipe wherein streamlines are all straight and parallel and the magnitude of the velocity is constant. 7) State whether the following are open or closed systems, give reasons for your answer. (6 marks) i) Rechargeable battery is a closed system because energy, but not matter, is exchanged with the environment. ii) Household refrigerator is an open system for both energy and matter can be exchanged with the environment (a fan circulates room air across the coil or tubes, and the refrigerant is totally vaporized, extracting heat from the air which is then returned to the food compartment). iii) Radiator is a closed system for energy (thermal energy), but not matter, is exchanged with the environment. 8) What is the difference between a gas, a liquid and a solid? (2 marks) In a gas the molecules are far apart and are moving at high speeds, colliding repeatedly with each other and with the walls of the container. In a liquid the molecules are packed more closely together, but still move rapidly, allowing them to slide over each other; thus, liquids pour easily. In a solid the molecules are held tightly together, usually in definite arrangements, in which the molecules can wiggle only slightly in their otherwise fixed positions. Thus, solids have rigid shapes. 9) What does thermodynamics tell us with regards to heat transfer? (1 mark) Thermodynamics tells us that we can relate the change in entropy to heat transferred during the process. For a process that occurs at constant temperature, the entropy change (dS) of the system is the value of heat transferred along a reversible path (dQ) divided by the absolute temperature (T). Therefore, when heat dQ enters or leaves a system at temperature T, it carries with it entropy in the amount dQ/T. 10) Explain the difference between internal energy (u) and enthalpy (h). (1 mark) Internal energy U is a FUNDAMENTAL property of matter. It is a function of state. A change of internal energy from state 1 to state 2 must be considered only in terms of the initial and final states; no route is specified. The term ΔU represents the change of internal energy of the system and is equal to q, thermal energy (‘heat’) added to the system PLUS won, the work done on the system. Enthalpy, on the other hand, is a DERIVED property of matter. It is a mathematical function defined in terms of fundamental thermodynamic properties as H = U + pV. Since H is a function of extensive state variables it must also be an extensive state variable. The change in enthalpy ΔH is equal to the heat q that flows in or out of a system during a thermodynamic process. 11) The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. (2 marks) 12) What is Fourier’s Law? What is n? Compare the values of thermal conductivity of metals, insulating materials and gases. What does Fouriers law have a minus sign? (10 marks) Fouriers law is an empirical law based on observation. It states that the rate of heat flow, dQ/dt, through a homogenous solid is directly proportional to the area, A, of the section at right angles to the direction of heat flow, and to the temperature difference along the path of heat flow, dT/dx: . Thermal conductivity n is a proportionality constant that characterizes how effectively substances can conduct heat. The SI units of n are W/m . K. Substances that are good thermal conductors have large thermal conductivity values, whereas good thermal insulators have low thermal conductivity values. Metals are generally better thermal conductors than insulating materials. Gases have very small thermal conductivities. The minus sign shows that heat always flows in the direction of decreasing temperature. 13) Explain the Stefan-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) Radiation is a means of energy transfer. All objects radiate energy continuously in the form of electromagnetic waves produced by thermal vibrations of the molecules. The rate at which an object radiates energy is proportional to the fourth power of its absolute temperature. This is known as the Stefan-Boltzman Law and is expressed in equation form as: where H is the heat current radiated by a surface area A, σ is a constant equal to 5.669 6x10-8 W/m2.K4, A is the surface area of the object in square meters, e is the emissivity constant, and T is the surface temperature in Kelvin. Emissivity (e) is a dimensionless number between zero and unity, representing the ratio of the rate of radiation from a particular surface to the rate of radiation from an equal area of an ideal radiating surface at the same temperature. It is generally assumed that all radiation leaving the small body would reach the large body. But in the case where two objects can see more than just each other, one must introduce a view factor F. The view factor F12 is used to parameterize the fraction of thermal (heat) power leaving object 1 and reaching object 2. It therefore makes heat transfer calculations become significantly more involved. An ideal absorber is defined as an object that absorbs all the energy incident on it, and for such a body, e = 1. Such an object is often referred to as a black body. An ideal absorber is also an ideal radiator of energy. 14) 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) Newtons Law of Cooling models the cooling (or heating) of an object which is placed in a surrounding medium. It states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. The heat transfer coefficient is used in calculating the  heat transfer, typically by convection or phase change between a fluid and a solid: ΔQ = heat input or heat lost, J 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 The Nusselt number is the ratio of convective to conductive heat transfer across (normal to) the boundary. It is a dimensionless number. The conductive component is measured under the same conditions as the heat convection but with (hypothetically) stagnant (or motionless) fluid: where L = characteristic length kf = thermal conductivity of the fluid h = convective heat transfer coefficient Energy transferred by the movement of a heated substance is said to have been transferred by convection. When the movement results from differences in density, as with air around a fire, it is referred to as natural convection. When the heated substance is forced to move by a fan or pump, as in some hot-air and hot-water heating systems, the process is called 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) The heat of combustion is the energy provided for a complete combustion of one gram of material. Heat release rate is the amount of thermal energy generated per unit of time or per unit of time per unit of area. A combustion reaction is when all substances in a compound are combined with oxygen, which then produces carbon dioxide and water. Combustion is commonly called burning. It is an exothermic reaction, which means heat is produced and is easily distinguished. The different types of combustion are as follows: Rapid combustion is a form of combustion in which large amounts of heat and light energy are released. Slow combustion is a form of combustion which takes place at low temperatures. In complete combustion, the reactant will burn in oxygen, producing a limited number of products. When a hydrocarbon or any fuel burns in air, the combustion products will also include nitrogen. For example, the combustion of methane in air will yield, in addition to the major products of carbon dioxide and water, the minor products which include carbon monoxide, hydroxyl, nitrogen oxides, monatomic hydrogen, and monatomic oxygen. Turbulent combustion is a combustion characterized by turbulent flows. Incomplete combustion happens when there is an inadequate supply of oxygen for combustion to occur completely. Incomplete combustion is much more common and will produce large amounts of byproducts, and in the case of burning fuel in automobiles, these byproducts can be quite unhealthy and damaging to the environment. Quality of combustion can be improved by design of combustion devices, such as burners and internal combustion engines. Smouldering combustion is a flameless form of combustion, deriving its heat from heterogeneous reactions occurring on the surface of a solid fuel when heated in an oxidizing environment. The specific heat capacity c of a substance is the heat capacity per unit mass:. Specific heat is essentially a measure of how thermally insensitive a substance is to the addition of energy. The greater a material’s specific heat, the more energy must be added to a given mass of the material to cause a particular temperature change. Different substances respond differently to the addition or removal of energy as they change phase because their internal molecular arrangements vary. Also, the amount of energy transferred during a phase change depends on the amount of substance involved. If a quantity Q of energy transfer is required to change the phase of a mass m of a substance, the ratio characterizes an important thermal property of that substance. Because this added or removed energy does not result in a temperature change, the quantity L is called the latent heat (literally, the “hidden” heat) of the substance. The value of L for a substance depends on the nature of the phase change, as well as on the properties of the substance. One technique for measuring specific heat involves heating a sample to some known temperature Tx , placing it in a vessel containing water of known mass and temperature Tw Read More