Energy Transfer and Thermodynamics - Assignment Example

Name of the Student] [Name of the Professor] [Name of the Course] [Date ] Energy Transfer and Thermodynamics Q. 1) Define the terms Thermodynamics and Energy A.) These terms are defined as follows: Thermodynamics That branch of science that is seized with the correlation between heat and other forms of energy is defined as thermodynamics. Simply stated, it constitutes the study of energy, energy transformations and their relation to matter (Energy, Enthalpy, and the First Law of Thermodynamics). Energy The transfer of energy constitutes work; and energy is the ability to do work. Energy is measured in Joules (J), in the SI system (The Physics Department - Mechanics, Energy). Q. 2) Explain what is meant by a physical system and distinguish between an open and closed system A.) A system comprises of a region in space or a quantity of matter that is subjected to scientific study. What is external to the system constitutes its surroundings. The boundary is a tangible or imaginary surface that segregates the system from its surroundings. Mathematically, the boundary has no thickness, and its mass and volume are zero. Its position can be either fixed or variable. For instance, if the mass in a system is not constant, then the boundary could change in extent, in order to take into account the variation in the mass. Open System In general, an open system, encloses a device that entails the flow of mass, an example is a compressor. Not only mass, but also energy can transit across the boundary of such a system. It is termed a volume controlled system, because the volume enclosed by the boundary is constant. Closed System When the mass in a system is precluded from crossing the boundary, and consequently, the mass in the system is constant, we have a closed system. However, it is possible for thermal energy and energy as work to be transferred across the boundary. In addition, it is inessential for the volume of a closed system to be constant (Cengel and Turner). Q.3) A heat rate of 3 kW is conducted through a section of an insulating material of cross sectional area 10m2 and thickness 2.5cm. If the inner (hot) surface temperature is 415°C and the thermal conductivity of the material is 0.2 W/mK, what is the outer surface temperature? A.) The relation between rate of heat conduction, area perpendicular to the conduction path and the temperature gradient is given by Fourier’s equation In the given problem  = 3kW = 3000W k = 0.2W/mK A=10m2 dx=2.5cm=0.025m Th = 415 °C = 415+273.15 = 688.15 K The linear temperature gradient  =  We are required to find the outer surface temperature TC Hence, TC = 688.15-37.5 = 650.65 K = 377.5 °C Hence the temperature of the outer surface is 377.5 °C. 4) Define the terms "Potential energy" and "Kinetic energy". A.) A definition of these terms is appended below. Potential Energy Potential energy is the energy stored or available for a body to do work. Kinetic Energy Kinetic energy is the energy possessed by a body due to its motion (Mulcrone). 5) State the four variables that are commonly used to quantify a gas. A.) Any gas can described in terms of four variables, namely: 1. Pressure (P) 2. Volume (V) 3. Temperature (T) 4. The amount of the gas (n) The ideal gas equation provides a relationship between these four variables. It is given by When P is measured in atmospheres, V is measured in liters, n is measured in moles and T is measured in Kelvin, the value of the ideal gas constant R = 8.314472 JK−1mol−1. 6) Please indicate if these statements are TRUE or FALSE: A.) a. The entropy of a gas increases with increasing temperature. (True) b. The energy of a perfect crystal is zero at 0 K. (False) c. Spontaneous processes always increase the entropy of the reacting system. (False) d. All spontaneous processes release heat to the surroundings. (False) e. An endothermic reaction is more likely to be spontaneous at high temperatures than at low temperatures. (True) f. The entropy of sugar decreases as it precipitates from an aqueous solution. (True) 7) Define the following terms as applied in thermodynamics: A.) a. Isothermal Process An isothermal process is a process in which the temperature of the system does not change. b. Intensive Property The intensive properties of a system are those that are independent of its mass; such as temperature, pressure, and density. c. State Function A property of a system that is independent of the manner in which the system gets into the state, in which it exhibits that property, is termed as a state function. It only depends on the current state of the system. d. Isolated System A system that is closed to the transfer of mass, heat and work is defined as an isolated system. Such a system is unaffected by its surroundings. 8) State the first and second laws of thermodynamics in words, and express it mathematically. A.) The First Law The first law of thermodynamics states that “The total energy of an isolated thermodynamic system is constant”. It is also referred to as the law of conservation of energy. In other words, the first law says that energy of a system changes in only two ways, either as work W or heat Q, the total energy U cannot change in any other way. Thus, for a finite change: ∆U=Q-W or dU=dQ-dW The Second Law The second law of thermodynamics, states that the total entropy of a system cannot decrease except insofar as the entropy flows outward across the boundary of the system. As a consequence, in an isolated system, the entropy cannot decrease (Farabee). 9) Define entropy. What are the units of entropy? A.) Energy and matter tend to become more disordered. Entropy, S, is defined as a measure of disorder. The increasing disorder in a system, accounts for spontaneous change. Entropy as energy, Q, in relation to absolute temperature, T, is expressed as S =  . Hence, its units are JK-1. 10) How does the entropy of a system change for each of the following processes? a. A vapour is converted to a solid A.) Entropy decreases b. A liquid freezes A.) Entropy decreases c. A liquid boils. A.) Entropy increases. 11) Define heat capacity and specific heat. What are the SI dimensions of these quantities? A.) The heat capacity, C, of a substance is the amount of heat required to change its temperature by one degree. It has the units of energy per degree. The heat capacity is therefore an extrinsic property, since it depends on the mass of the substance under investigation. The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. This relationship does not hold good if a phase change transpires; because the heat added or removed during a phase change, does not change the temperature. Therefore, unlike the extrinsic variable heat capacity, which depends on the quantity of material, specific heat is an intrinsic variable and has units of energy per mass per degree or energy per number of moles per degree. The SI dimensions of heat capacity is joule per kelvin: J/K = m2 kg s-2 K, whilst specific heat has the SI dimensions of joule per kilogram kelvin: J/kg.K = m2s-2 K 12) Briefly describe the absolute temperature scale. A.) The absolute temperature scale is characterised by a zero that corresponds to the theoretical absolute zero of temperature or the thermodynamic equilibrium state of minimum energy. In SI units, temperature is measured on the Kelvin (K) scale. That temperature, at which water can be maintained in the solid, liquid and vaporous states is the only point established by arbitrary definition, in the Kelvin scale. By definition, an interval of 273.16 K is deemed to exist between the absolute zero and this temperature. Thus, this so called triple point’s temperature is designated as 273.16 K. Essentially, the Kelvin scale is the Celsius scale shifted by 273.15 degrees, on account of the fact that the triple point of water is 0.01 °C, with the same sized temperature units. The Rankine (°R), is an additional absolute temperature scale. It is based on the Fahrenheit (°F) temperature scale, with the freezing point of water defined as 491.67 °R. A degree Rankine, is 9/5 of a Kelvin or degree Celsius (absolute temperature scale). 13) Does Heat depend on the Mass of a Substance? Does Temperature depend on the Mass of a Substance? A.) The amount of heat energy, possessed by a substance depends on its mass. If the mass is doubled, twice the amount of heat energy will be required to heat it to the same temperature. Temperature is a measure of the kinetic energy of the particles, in other words their speed; it is independent of the mass of the substance, or the number of particles. 14) Name and describe three forms of energy. A.Thermodynamics, envisages three forms of energy. These are described in the sequel. Potential Energy, Ep The energy possessed by a body by virtue of its position is termed the potential energy, Ep. Kinetic Energy, Ek The energy associated with a body, on account of its motion is termed its kinetic energy, Ek. It is possible for a body in motion to perform work, whenever it is made to slow down or brought to a standstill. Rest Energy, Er Albert Einstein introduced the concept of the rest energy of a body, by means of his Special Theory of Relativity. This rest energy, Er is that energy possessed by a body due to its mass. It can be evaluated by means of the famous equation: Er = mc2. Where m is the mass of the body at rest, and c the velocity of light. The total energy, E possessed by any macroscopic body or system is given by E = Ep + Ek + Er. (Anderson and Crerar) 15) Calculate ∆So for the following reaction, using the information in the table of thermo chemical data provided, 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) . A.) The standard molar entropies of reactants and products are So (NO) = 210.76 JK−1mol−1 So (O2) = 29.378 Jmol−1K−1 So (N2O4) = 150.38 JK−1mol−1 ∆ So = Σ So(Products) - Σ So(Reactants) ∆ So = So (N2O4) – 2 × So (NO) - So (O2) ∆ So = 150.38 JK−1mol−1 - 421.52 JK−1mol−1 – 29.378 JK−1mol−1 = -300.52 JK−1mol−1 The entropy decreases in this reaction and thus this reaction can be assumed to be a non – spontaneous reaction. 16) These questions test your understanding of temperature measurements and temperature scales. i)What is absolute zero on the Kelivin, Celsius, Fahrenheit and Rankine scales? A.) The absolute zero is the zero of the Kelvin and Rankine temperature scales. In the Celsius scale it is -273.15 °C and in the Fahrenheit scale it is -459.67 °F ii) Human body temperature is 37°C what is this in Kelvins? A.)The temperature of the human body in the Kelvin scale is 37 OC = 37 + 273.15 = 310.15K . iii) The temperature of a system rises by 60°C during a heating process. Express this rise in temperature in Kelvins. A.) A degree Kelvin is the same as a degree Celsius, and the difference, betwixt them exists only in the absolute point’s position. Consequently, a 60°C increase in temperature, corresponds to a 60K rise in temperature. iv) The temperature of a system rises by 60°F during a heating process. Express this rise in temperature in R, K and °C. A.) One degree Fahrenheit is equivalent to a degree Rankine; therefore a temperature increase of 60°F, is represented by 60 R on the Rankine scale. One degree on either the Kelvin or Centigrade scale is 5/9th of a degree on the Rankine or Fahrenheit scale. Consequently, the increase in temperature is given by  C° or 33.33 K. 17) The mass flow rate is 2kg/s, the heat of combustion for C3Hs is 46450kJ/kg. Determine the heat release rate. A.)In respect of simple objects, composed of a pure substance, and possessing heat of combustion that is constant and known; measurement of the rate of heat release, is restricted to measurement of the rate of loss of mass. This is due to the fact that the rate of loss of heat is proportional to the rate of lass of mass. Mathematically, Where  the measured rate of heat release is, is the mass loss rate, and HC is the known lower heat of combustion, in kJ/kg. Here  = 2kg/s,  is 46450 kJ/kg, and  is to be determined. kJ/s. Hence the rate of release of heat is 92900 kJ/s. 18) What is Fourier's Law? What is thermal conductivity? Compare the values of thermal conductivity of metals, insulating materials and gases. Why does Fourier's law have a minus sign? A.)According to Fourier’s law, the rate of conduction of heat per unit cross – sectional area of a body is proportional to the negative temperature gradient of the body. Heat flow is in the direction of the negative temperature gradient; consequently, it flows from a hotter body to a colder body. This justifies the negative sign in Fourier’s equation which is given below: QCond =  The proportionality constant k in the Fourier’s equation is termed the thermal conductivity of the material (Mortimer). It is a measure of the ability of a substance to conduct heat, and it is measured in w/m-K. The range of values assumed by k for metals, insulators and gases is provided below in a tabular form. Type Of Material Thermal Conductivity Value Metals 52 ~ 415 w/m-K Insulating materials 0.035 ~ 0.173 w/m-K Gases 0.0069 ~ 0.173 w/m-K 19) Heat Radiation is what type of wave? Explain the Stefan-Boltzmann Law. What is emissivity? What role does the view factor play in determining the rate of heat transfer? A.) Heat radiation is an electromagnetic wave that propagates as a transverse wave. The Stefan – Boltzmann law relates the maximum amount of radiation that can be emitted per second and the absolute temperature of the surface (TS) from which it is emitted. Qe(max) = ATS4 Where Qe(max) is the amount of radiation emitted per second, A is the area of the radiating surface, TS is the absolute temperature of the surface in Kelvin and  a constant of proportionality, which is known as Stefan’s constant. = 5.67 × 10-8 W/m2-k4 (Sturge) The relation given above, pertains to an ideal radiator or blackbody. However, the reality is otherwise, and there are no ideal radiators. This situation, necessitated the definition of a more relevant constant, termed emissivity (ε), defined as the ratio of energy radiated by the material to energy radiated by a black body at the same temperature. Hence, ε = ε is a dimensionless quantity that depends on temperature at which it is measured and the material. For an ideal radiator or blackbody, ε = 1; for all other real surfaces 0< ε Read More