Engineering Trans and Thermodynamics - Assignment Example

Name of the Student] [Name of the Professor] [Name of the Course] [Date] Thermodynamics 1).Define the terms thermodynamics and energy. Answer. Thermodynamics: A branch of physics that describes the conversion of energy into heat and work. It correlates the physical properties of macroscopic systems, like matter and energy, s temperature, volume, and pressure. Energy: It describes the amount of work that can be performed by a system. Its SI units are joules (Tschoegl). 2). Explain what is meant by a physical system and distinguish between an open and closed system Answer. System: In a thermodynamic system, a working substance is defined as that part of the universe that is under consideration. A hypothetical boundary separates the system from the rest of the universe, which is referred to as the environment, surroundings, or reservoir of the system. Open System: Matter and energy can be interchanged between the system and its surroundings. Closed system: Energy can be exchanged between the surroundings and system, but the amount of matter in the system remains constant system (Yates and Johnson). 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? Answer. Qx = 3kW, A = 10 m2, t = 2.5, Th = 415oC, k = 0.2W/m K, Tc = ? Assumption 1. Steady State Condition 2. Thermal conductivity is constant and independent of temperature. 3. One – dimensional conduction Fourier’s Law states that At steady state qx is constant, Hence, Tc = 40oC. 4). Define the terms "Potential energy" and "Kinetic energy". Answer. Potential energy: Potential energy is defined as the stored energy in a physical system Kinetic energy: Kinetic energy is the energy associated with the motion of a body. 5) State the four variables that are commonly used to quantify a gas. Answer. The four variables used to quantify a gas are : I)Pressure II)Volume III)Temperature IV)Amount 6) Please indicate if these statements are TRUE or FALSE: 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. Isothermal process: A process that transpires at constant temperature is referred to as an isothermal process. b. Intensive property: The value of an intensive property is independent of the amount of material present. For example: temperature; pressure; and density of a substance. c. State function: The value of a particular property for a system depends on the state of that system, it is referred to as a state function. For example; pressure, volume, internal energy and entropy. d. Isolated system: A system in which neither matter nor energy can be exchanged with the surroundings (Engineers Edge). 8) State the first and second laws of thermodynamics in words and express it mathematically. Answer. The First Law: The first law of thermodynamics states that “The total energy of an isolated thermodynamic system is constant”. The law is often referred to as the conservation of energy。In other words, energy maybe lost from a system in only two ways, either as work or as heat, U cannot change in any other way. Thus, for a finite change: ΔU=Q-W or dU=dQ-dW Heat: Let Q denote the heat. Q is positive if heat is gained by system, and Q is negative if heat is lost by the system. Work: Let W signify work. Then W is positive if the work is done by system while expanding, and W is negative if the system is compressed. When a reaction releases a gas at a constant external pressure Pex, the work done is given by: W= Pex ΔV or dW= Pex dV. Second law: The second law of thermodynamics, states that the total entropy of any system cannot decrease except insofar as it flows outward across the boundary of the system. As a corollary, in an isolated system, the entropy cannot decrease (the second law places no restrictions on the increase of entropy) (Farabee). 9) Define entropy. What are the units of entropy? Answer. Entropy, is a measure of distribution of energy in a system, it is measured in units of J mol-1 K-1, that is, joules per mole per kelvin.It can be seen as the amount of randomness in a system. The entropy of a system is given by the equation: S = k ln w where S is entropy, k is the Boltzmann constant and w is the number of ways of arranging the energy in the system(Engineers Edge). 10) How does the entropy of a system change for each of the following processes? a. A vapour is converted to a solid, b. A liquid freezes, c. A liquid boils. Answer. a.Entropy decreases b.Entropy decreases c.Entropy increases. 11) Define heat capacity and specific heat. What are the SI dimensions of those quantities? Answer. The heat capacity C of a substance is the amount of heat required to change its temperature by one degree, and has units of energy per degree. The heat capacity is therefore an extensive variable since a large quantity of matter will have a proportionally larger heat capacity. Its SI units are J/oC. A more useful quantity is the specific heat (also called specific heat capacity), which is the amount of heat required to change the temperature of one unit of mass of a substance by one degree. Specific heat is therefore an intensive variable and has units of energy per mass per degree. Its SI units are J/Kg/ oC. 12) Briefly describe the absolute temperature scale. Answer. Absolute temperature scale is a temperature scale where the minimum temperature is zero. In other words, there are no negative values of temperature. Two absolute scales are the Kelvin scale in which each division is of the same length as that in the Celsius scale; and the Rankine scale, in which each division is as long as a division in the Fahrenheit scale (absolute temperature scale). 13) Does Heat depend on the Mass of a Substance? Does Temperature depend on the Mass of a Substance? Answer. The amount of heat energy which a substance possesses depends on its mass. If the mass is doubled, the heat energy required to heat it to the same temperature is doubled. Temperature is a measure of the kinetic energy of the particles. Or an indication of how fast the particles are moving. Temperature does not depend on the mass of the substance, in other words it is independent of the number of particles in the system (France). 14) Name and describe three forms of energy. Answer. The three forms of energy are; Work W, is the amount of useful energy transferred across a system's boundaries, and which has the capacity to invoke macroscopic mechanical motion in the center of mass of the system. Heat Q, this is the energy transferred across a system’s boundary, but it is incapable of bringing about macroscopic mechanical motion of the centre of mass of the system. Internal Energy U, which indicates a system’s stored energy at the molecular level. This is comprised of the system’s thermal energy and its binding energy (WORK - W, HEAT - Q, and INTERNAL ENERGY - U). 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) Answer. 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) = 150.38 JK−1mol−1 - 421.52 JK−1mol−1 – 29.378 JK−1mol−1 ∆ So =-300.52 JK−1mol−1 Hence the entropy decreases in this reaction. Based on entropy changes, this reaction will 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? ii) Human body temperature is 37C what is this in Kelvins? iii) The temperature of a system rises by 60°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. i) The absolute zero in the zero of the Kelvin and Rankine temperature scales. Absolute zero is -273.15 degrees Celsius and -459.67 degrees Fahrenheit. ii)We know that 0°K = 273.15 oC and that one degree Celsius equals one degree Kelvin. Hence, we add 273.15 to the degrees in centigrade to obtain the temperature in degrees Kelvin. Therefore, the Kelvin equivalent of 37 OC = 37 + 273.15 = 310.15°K Hence temperature of human body is 310.15° K. III) One degree Celsius is equal to one degree Kelvin (The only difference between these scales lies in the situation of the absolute point). Hence an increase of 60°C is equivalent of a rise in temperature of 60°K. IV) A Rankine degree is defined as equal to one degree Fahrenheit. Hence the equivalent rise of 60°F in the rankine scale is 60° R. To convert this rise in Fahrenheit to a rise on the Celsius scale, we first subtract 32O and multiply the result with 5/9.  hence  = (60-32) ×  = 28 ×  = 15.55°C. Hence, a 60°F rise in temperature is equivalent to a rise of 15.55 OC Since one degree Kelvin is equal to one degree centigrade, the same rise in temperature is registered in the Kelvin scale as in the centigrade scale. Hence a 60°F rise in temperature is equivalent to a rise of 15.55° K. 17) The mass flow rate is 2kg/s, the heat of combustion for C3Hs is 46450kJ/kg. Determine the heat release rate. Answer. Heat release rate (q’)= heat of combustion(HC) X mass flow rate(m’’’) = 46450 kJ/kg X 2 kg/s =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. What does Fourier's law have a minus sign? Answer. Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in temperature and the area at right angles to the temperature gradient. i.e  By introducing a proportionality constant k, called thermal conductivity, we obtain  where  = the time rate of heat transfer and k is a constant called the thermal conductivity of the substance which is an intrinsic property. A is the cross sectional area through which the heat transfer takes place and  is the temperature gradient. The above equation is known as Fourier’s equation. Thermal conductivity is an intrinsic property of a material, which indicates its ability to conduct heat. It is denoted by k . From Fourier’s law we write  It is measured in units of  In general metals have high thermal conductivity, in the region of 50-400 Wm-1K-1. Insulators such as foam plastics and rubbers have thermal conductivity in the region of 0.03-0.06 Wm-1K-1. The conductivity of gases is even lower .At 0oC air has a thermal conductivity of 0.024 Wm-1K-1. Heat flows from a hotter body to a colder body that is in the direction of the negative temperature gradient. Thus a minus sign should appear in Fourier’s equation (Fourier Law of Heat Conduction ). 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? Answer. Infra-red radiation transfers heat between all objects. It is an electromagnetic wave and can travel through vacuum. Heat from the Sun reaches us through the vacuum of space by travelling as infrared radiation. The energy radiated by a blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature. It is given by the equation:  = σT4 j/m2s, where σ = 5.6703× 10-8watt/m2K4. This constitutes the Stefan – Boltzmann Law. In respect of non – ideal radiators, this law assumes the form:  = eσT4 , Where e is the emissivity of the object, which is 1 for ideal radiators. As such, emissivity is the ratio of the radiation emitted by a blackbody or surface to the theoretical radiation derived from Planck’s law(Stefan-Boltzmann Law). 20) 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? Answer. Newton’s Law of Cooling defines the relationship between the rate of energy flow at the interface of a fluid and solid object, due to heat transfer by convection. If the surface temperature of the solid is denoted by Ts and the bulk fluid temperature as T∞, then the required energy transfer rate between the fluid and the solid is proportional to the surface area for heat transfer A and the difference in temperature between the solid surface and the bulk fluid temperature. The letter h is employed to denote the constant of proportionality, which is termed as the coefficient of heat transfer. As an equation, Newton’s Law of Cooling can be stated as q = hA (Ts - T∞) ------- (1) The assumption here is that energy flows from the solid to the fluid. As W =J/s = (units of h)(m2)(°C) The units of h the heat transfer coefficient are given by W/m2°C, and q the rate of energy transfer has the units of W. In general, q is divided by the area of heat transfer. This yields the following equation: q” = = h (Ts - T∞) ------- (2) In heat transfer at surfaces within a fluid, the Nusselt number constitutes the ratio between convective and conductive heat transfer normal to the boundary (White). Convection is a heat transfer mechanism, which involves the motion of molecules. It is the cardinal method of heat transfer, on our planet. It is of great significance for engendering different weather conditions (McGuigan). The two types of convection are, first forced convection that transpires when the heat transferring medium moves of its own accord. For instance, air pushed by a cooling fan. It is also known as heat advection. Second, natural convection, which occurs, when the heat transferring medium moves on account of the heat that it transfers. It is also known as natural convection and occurs when a gas expands, on being heated(McGuigan). 21) Define heat of combustion and heat release rate. Answer. ΔHc° the heat of combustion is the amount of energy that is released as heat, on the complete combustion or one mole of a compound. It can be expressed in any of the following ways: Energy /mole of fuel (J/mol) Energy / mass of fuel Energy / volume of fuel (Heat Release Rate). 22) Define the terms premixed flame and diffusion flame. When the oxidizer is mixed with the fuel, prior to reaching the flame front, it is known as a premixed flame. The outcome is a thin flame front as all the reactants are readily available. On the other hand, a flame in which the oxidizer combines with the fuel by diffusion is a diffusion flame. In such flames, the speed of the flame is subject to the diffusion rate. 23) What is the difference between Newtonian and Non-Newtonian fluids? How does temperature affect viscosity? Answer. When the viscosity of a fluid depends on the applied stress, it is termed as non – Newtonian. A common example of such fluids is provided by an aqueous solution of cornstarch. A Newtonian fluid is one whose behaviour can be expressed completely by its temperature and pressure. This behaviour is independent of the forces acting on the fluid. Water is a common example of a Newtonian fluid. The viscosity of a liquid is inversely proportional to increase in its temperature; whereas, the viscosity of a gas is directly proportional to increase in its temperature. This holds good for low and moderate pressures(Anissimov). 24) Will an object emit radiation faster with a matt or a shiny surface? Will an object emit Radiation faster with a dark or a light surface? Answer. Whenever, an object possesses a dull surface, it will prove to be a better absorber and emitter of infrared radiation, in comparison to an object with a shiny surface. Infrared radiation is absorbed and emitted much faster by an object that possesses a dark surface than an object with a light surface. Moreover, radiation undergoes reflection at the surface. 25) The temperature of a sample of water increases by 69.5 °c when 24 500 J are applied. The specific heat of liquid water is 4.18 J/g × oC. What is the mass of the sample of water? Answer. Here, q=24500J c=4.18 J/g × oC ∆T=69.5 oC We know that q=mc∆T Hence m=q/c∆T m=24500/(69.5 × 4.18 ) =84.33g. Hence, the mass of the sample of the water is 84.33 grams. Works Cited absolute temperature scale. 19 August 2009 . Anissimov, Michael. What is a Non-Newtonian Fluid? 2 May 2009. 19 August 2009 . Engineers Edge. Thermodynamics Definitions and Terminology. 19 August 2009 . Farabee, M.J. LAWS OF THERMODYNAMICS. 2001. 19 August 2009 . Fourier Law of Heat Conduction . 19 August 2009 . France, Dr. Colin. Energy Transfer. 2008. 19 August 2009 . Heat Release Rate. 2008. 19 August 2009 . McGuigan, Brendan. What is Convection? 2003. 19 August 2009 . Stefan-Boltzmann Law. 19 August 2009 . Tschoegl, Nicholas W. Fundamentals of equilibrium and steady-state thermodynamics. Elsevier, 2000, P 3-5. White, Dr. J. R. Newton's Law of Cooling. August 1998. 19 August 2009 . WORK - W, HEAT - Q, and INTERNAL ENERGY - U. 19 August 2009 . Yates, John T. and J. Karl Johnson. Molecular physical chemistry for engineers . University Science Books, 2007, Pp 2 - 4. Read More