Energy Transfer and Thermodynamics - Assignment Example

1) Define the four laws of thermodynamics using words, diagrams and equations where appropriate. (8 Marks) Suppose three systems 1, 2 and 3 are in an adiabatic enclosure as shown in the diagram below. Systems 1 and 2 are separated using an adiabatic wall hence do not interact with each other, but system 1 and 2 interact separately with system 3 through a diathermal wall so that system 1 is in thermal equilibrium with system 3, and system 2 is also in thermal equilibrium with system 3. Therefore the zeroth law of thermodynamics is stated as “if each of the two given systems 1 and 2 are in thermal equilibrium with a third system 3, then the two systems 1 and 2 are in thermal equilibrium with each other (Jones, 1910) Fig. A sketch illustrating the zeroth law of thermodynamics. The first law of thermodynamics states that energy is conserved. It can neither be created nor destroyed. The internal energy of a system, U0, changes to a final value, U1, when heat, Q, is released or absorbed by the system and the system does work, W, on its surroundings (or the surroundings do work on the system),such that U1-U0=∆U=Q-W. According to Clausius, the second law of thermodynamics reads “it is impossible to construct a device that, working cyclically, will produce no other effect than the transfer of energy in the form of heat from a low temperature body to a high temperature body” (Rao, 2004, p. 210). This law denies the possibility of self reversal of spontaneous process. The third law of thermodynamics is stated as “it is impossible by any procedure, no matter how idealized, to reduce the temperature of any system to the absolute zero in finite number of operations.” 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, S, refers to the measure of the disorder of a system. Ice melts when it absorbs thus increasing the kinetic energy of the molecules. When ice melts, the molecules gain energy and move far apart, making it less organized. This results to an increase in the entropy of the system (Moran and Shapiro, 2006). 3) Predict whether entropy will be 0 for the following processes: (3 Marks) a. Dry ice melts, ∆s>0 b. Water freezes, ∆s0 4) Calculate ΔS for the following reaction, using the thermodynamic data provided. Substances                S0 (J/K.mol) CH4 (g)                         186 O2 (g)                            205 CO2 (g)                         214 H2O (l)                            70 N204 (g) 304 NH3 (g) 193 N2 (g) 192 H2 (g) 131 NO (g) 211 (6 Marks) ΔS0reaction = ΣnpS0 (products) – ΣnrS0 (reactants) Where np represents the number of moles of each product and nr represent the moles of each reactant. a. 2NO (g) +O2 (g) → N2O4 (g), ∆S0 = [304]-[(2*211) +205] = -321 J/K b. 3H2 (g) + N2 (g) → 2NH3 (g), ∆S0 = [2*193] – [(3*131) +192] = -199 J/K c. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l). ∆S0 = [214+ (70*2]-[186+ (205*2)] =-242 J/K 5) These questions test your understanding of temperature measurements and temperature scales. (8 Marks) a. Body temperature is 37°C what is this in Kelvin, Fahrenheit and Rankine scales? t 0F = (9/5)* t +32; t °C = temperature in °C, t 0F = temperature in 0F [K] = [°C] + 273.15 [°R] = [K] *9/5 37°C in Kelvin scale will be (37+273.15) K = 301.15K 37°C in Fahrenheit will be [(9/5)* 37 +32]0F =98.60F 37°C in Rankine will be [(37+273.15)*9/5] °R =542.07°R b. What is absolute zero in Celsius, Fahrenheit and Rankine scales? Absolute zero is 0K; in Celsius it will be [K] − 273.15; [°C] =0-273.15 =-273.15°C 0K in Fahrenheit; [°F] = [K] * 9⁄5 − 459.67; [°F] = (0*9/5)-459.67=)-459.670F 0K IN Rankine; [°R] = [K] *9⁄5; 0*9⁄5= 0°R c. The temperature of a system rises by 35°C during a heating process. Express this rise in temperature in Kelvins. For a rise, 1K = 1°C; therefore, a rise of 35°C will be a rise of 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. For a rise, 1°F = 1°R; therefore, a rise of 80°F will be arise of 80°R For a rise, 1°F=10/18 K; therefore a rise of 80°F will be (5/9)*80= 444/9K or 44.44 K (in 2 d.p) For a rise, 1°F=1°C; therefore a rise of 80°F will be (5/9)*80= 444/9°C or 44.44°C (in 2 d.p) 6) The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. (1 Mark) Heat release rate = mass flow rate*enthalpy of combustion; 4*46450= 185800 kilowatts 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 states that the rate of heat transfer per unit area normal to the direction of heat flow is directly proportional to the temperature gradient (Nag, 2010). Mathematical expression of Fourier’s law is q = Q/A = -kdT/dx or Q=-kAdT/dx where, q is the heat flux, dT/dx is the thermal gradient in the flow direction, k is thermal conductivity, Q is rate of heat transfer in W, and A is the heat transfer area in m2. The SI unit of q is watts per meter squared (w/m2) Thermal conductivity is the ability of a substance to conduct heat through it i.e. the rate of heat transfer through a unit thickness of material per unit area per unit temperature difference (Moran and Shapiro 2006). Thermal conductivity of substances is highest in solid phases as compared to gaseous phases. Pure metals have highest thermal conductivity hence they are referred to as good conductors. Most non-metals are poor conductors of heat transfer and thus, they have low values of thermal conductivity. Therefore, they are called thermal insulators. The minus sign in Fourier's law shows that the heat flows from a hotter point to a colder point. 8) Explain the Stefen-Boltzman Law. What is emissivity? What is the range 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-Boltzman Law states that the radiating heat flux or emmissive radiations is proportional to the fourth power of temperature on absolute scale. Thus E b= (q/A) =σT4; where A is the surface area in m2, T is temperature, Eb is the radiating heat flux, q is the rate of heat transfer in watts and σ is Stefan-Boltzmann constant (5.669×10-8 W/m2K4)( Moran and Shapiro, 2006) Emissivity is the ration of the amount of radiation given off by a surface to that emitted by an equally sized blackbody at the same temperature. The values of emissivity range from zero to one. A black surface is a surface that cannot transmit any radiation (t=0) because they emit all possible radiation at a given time. A grey surface is a surface with emissivity being independent on both the wavelength and angle of emission. The view factor represents the fraction of radiation that leaves one surface and strikes another surface. A black body is an idealized body which absorbs all the incident electromagnetic radiation. 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 refers to the heat liberated when one mole of the substance undergoes a complete combustion with oxygen at constant pressure. According to Kothandaraman and Subramanyan (2008), heat release rate refers to the amount of heat released by a burning substance and is recorded in Kw. The total heat release rate is obtained by adding the contributions from each part of t the burning area and the burner. Q total =Q product +Q burner Combustion reaction is a chemical reaction which involve oxygen and produce energy (heat) so rapidly resulting into a flame. An example is CH4 (g) +2O2 (g) =CO2 (g) +2H2O (g) The types of combustion include burning and smouldering. Burning refers to the direct combination of oxygen and other substance as a result of an external source of heat. Smouldering is a slow but steady, low temperature and flameless type of combustion that is sustained by the heat energy evolved after oxygen attacks a surface of a condensed phase fuel. The specific heat capacity, (Cg) of a substance refers to the amount of heat required to raise unit mass of the substance by one degree of temperature. Latent heat refers to the amount of heat absorbed or released by a substance when undergoing a change of state, for example, ice changing to water or water to steam, at constant pressure and temperature. Calorimetry refers to the experimental determination of the enthalpy changes that accompany chemical reactions by use of direct methods, i.e. calorimeters. Combustion temperature refers to the temperature in the combustion chamber and it is given in degrees Kelvin Chemical equilibrium is the state when there is a constant ratio on concentration of products and reactants in a chemical reaction hence there is no net change over time. 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) E b=σT4; E = 5.669×10-8 W/m2K4 *(20+273) K4 =4.18X102W/m2. It is a god emitter of radiation. 11) Does heat depend on the mass of a substance? Does temperature depend on the amount of a substance? (2 Marks) Heat energy of a substance depends on it mass. The temperature of a substance does not depend on the amount of substance. 12) How is natural convection different from forced convection? (2 Marks) In natural convection, the motion of the adjacent fluid is caused by buoyancy forces that are induced by the density difference due to variation of temperature in the fluid. In forced convection, the fluid is forced to flow overs a solid surface by external means such as a pump or a fan. 13) Aluminium has a specific heat of 0.902 J/g 0C. How much heat is lost when a piece of aluminium with a mass of 23.984 g cools from a temperature of 415.00C to a temperature of 22.00C? (2 Marks) q = m * Cg *(Tf - Ti) q = 23.984g *0.902 J/g 0C *(22-415)0C; 23.984*0.902*-393 = -8501.99J Therefore, amount of heat lost is 8501.99J 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) Maximum efficiency= (T hot-T cold)/T hot ; [(300+273)-(10+30)]/(300+273)= 533/573 =0.93 or 93% 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/g oC. What is the mass of the sample of water? (2 Marks) q = m * Cg *(Tf - Ti) 24 500 J= m*4.18 J/g oC *69.5 oC; 24500/ (4.18*69.5) =84.33444632 =84.33g 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) q = m * Cg * (Tf - Ti); q=70g*0.385J oC -1 g-1*30 oC = 805.5J 17) Define the following terms: (2 Marks) a. Heat capacity, CP, is the amount of heat required to raise the temperature of a substance by 1K. b. Specific heat, Q, is the amount of heat per unit mass required to raise the temperature by 10C. 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) dE = q + w where dE = Efinal - Einitial; since work is done by the system, we treat it as a negative. Therefore, 7J = q +-26J; q= 7+26= 33J 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) (Cp of iron = 0.45J/g0C q = m (DT) Cp; q=60000g*(152-22) 0C *0.45J/g0C; q = 3564000J or 3564Kj 20) 180J of heat is 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) Efficiency = Work output / Work input x 100%; efficiency = 40/180*100= 22.22% 21) What is kinetic energy and how does it relate to the temperature of a system? (2 Marks) Kinetic energy is the amount of energy possessed by a substance because of its motion. This amount of energy causes the temperature of the system to rise. 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) Let the final temperature be y; Q = m (milk)*specific heat capacity (milk)* Δt =m (coffee)*specific heat capacity (coffee)* Δt 1m3 =1000000ml; so 61.6 ml is equivalent to 0.0000616m3; mass =density *volume, so mass of milk= 0.0000616m3*1032000g/m3 =63.57g 1m3 =1000000ml; so 455.5 ml is equivalent to 0.0004555m3; mass =density *volume, so mass of coffee=0.0004555m3*1000000g/m3 =455.5g Q=63.57g*1.97 J/g °C*(y-18.6)°C= 455.5g*4.186 J/g °C*(90.2-y)0C; 125023(y-18.6)= 1906.72(90.2-y); y-18.6=1373.75-15.23; 16.23y= 137.75; thus the equilibrium temperature is 84.6 0C 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) specific heat capacity of water is 4.186 joule/gram °C. Let the final temperature be y; Q = m (cold water)*specific heat capacity* Δt =m (hot water)*specific heat capacity* Δt 1500g*4.186 j/g °C* (y-4) °C = 1500g*4.186 j/g °C*(65-y) °C; y-4=65-y; 2y=69; therefore the equilibrium temperature is 39.5°C 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) Q = mass*Δt * specific heat (gold); 1.33J=5g* Δt*0.129J/g °C; Δt= 1.33/0.129= 10.30C 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) ΔE = q + we take w to be negative because it is the gas does work; i.e. ΔE=2.5+-1.5J =1J 26) Explain the ideal gas law, give the mathematical equation and define all the terms used. (2 Marks) Ideal gas law is a law that relates the temperature, pressure and volume of an ideal gas. It given by the equation, PV=nRT where P= absolute pressure in atm, V= volume, n= number of moles of gas present R= ideal gas constant (R=0.082058 L atm mol-1 K-1) and T is absolute temperature in kelvins (Kothandaraman and Subramanyan 2008). 27) Explain what intensive and extensive properties are, giving examples of each to support your answer. (1 Mark) Intensive properties are thermodynamic properties that are independent of the amount of mass present. Examples are pressure, temperature and density (Kaviany, 2002). Extensive properties are the thermodynamic properties that depend on the amount of mass present. Examples include mass, weight and total volume (Kaviany, 2002). 28) Explain Newton’s Law of cooling and give the mathematical equation defining all the terms used. (2 Marks) Newton’s Law of cooling states that the rate at which the temperature T(t) changes in a cooling body at time t is proportional to the difference between the temperature of the body, T, and the constant temperature TS, of the surrounding medium. Mathematically, it can be presented as; dT(t)/dt k (T-TS ), T(0) =T0. 29) Discuss the different types of systems encountered in thermodynamics. (3 Mark) Kaviany (2002) explains the three types of systems as below; Open systems are those systems that can exchange both energy and matter with the surrounding. Therefore, the energy and matter do not remain constant in an open system. Closed systems are systems that can only exchange the energy with the surrounding while the transfer of matter to and from the surrounding is not possible. Therefore, it is only energy that changes in a closed system but the mass remains constant. Isolated systems are those systems that prevent any interaction with the surroundings. Consequently, both the energy and the mass remain constant. 30) Discuss the variables that are used to quantify a gas. (2 Marks) Volume, V; it refers to the 3D space that is enclosed by a container and this is the space that the gas occupies. The standard unit is Litres, L. Pressure, P; refers to the force exerted by a gas per unit area on the walls of its container. The standard unit is atm. Temperature, T; it refers to the heat energy that the gas has. The amount of gas, this variable can presented using the number of moles or the mass. The thermodynamic state of a gas can be specified using volume, temperature and pressure. References Jones, HC 1910, Introduction to physical chemistry, Macmillan Company, London Kaviany, M 2002, Principles of heat transfer, Wiley-IEEE, Great Britain Kothandaraman, CP and Subramanyan, S 2008, Fundamentals of heat and mass transfer, 3rd ednb, New Age International, New Jersey Moran, MJ and Shapiro, HN 2006, Fundamentals of engineering thermodynamics, 5th edn, John Wiley and Sons, USA Nag, H 2010, Basic & Applied Thermodynamics, 2nd edn, Tata McGraw-Hill, Delhi Rao, C 2004, An introduction to thermodynamics, Universities Press, New York. Rathore, R and Kapuno N 2010, Engineering heat transfer, 2nd edn, Jones & Bartlett Learning Canada. Read More

3) Predict whether entropy will be 0 for the following processes: (3 Marks) a. Dry ice melts, ∆s>0 b. Water freezes, ∆s0 4) Calculate ΔS for the following reaction, using the thermodynamic data provided. Substances                S0 (J/K.mol) CH4 (g)                         186 O2 (g)                            205 CO2 (g)                         214 H2O (l)                            70 N204 (g) 304 NH3 (g) 193 N2 (g) 192 H2 (g) 131 NO (g) 211 (6 Marks) ΔS0reaction = ΣnpS0 (products) – ΣnrS0 (reactants) Where np represents the number of moles of each product and nr represent the moles of each reactant. a. 2NO (g) +O2 (g) → N2O4 (g), ∆S0 = [304]-[(2*211) +205] = -321 J/K b. 3H2 (g) + N2 (g) → 2NH3 (g), ∆S0 = [2*193] – [(3*131) +192] = -199 J/K c. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l).

∆S0 = [214+ (70*2]-[186+ (205*2)] =-242 J/K 5) These questions test your understanding of temperature measurements and temperature scales. (8 Marks) a. Body temperature is 37°C what is this in Kelvin, Fahrenheit and Rankine scales? t 0F = (9/5)* t +32; t °C = temperature in °C, t 0F = temperature in 0F [K] = [°C] + 273.15 [°R] = [K] *9/5 37°C in Kelvin scale will be (37+273.15) K = 301.15K 37°C in Fahrenheit will be [(9/5)* 37 +32]0F =98.60F 37°C in Rankine will be [(37+273.15)*9/5] °R =542.07°R b. What is absolute zero in Celsius, Fahrenheit and Rankine scales?

Absolute zero is 0K; in Celsius it will be [K] − 273.15; [°C] =0-273.15 =-273.15°C 0K in Fahrenheit; [°F] = [K] * 9⁄5 − 459.67; [°F] = (0*9/5)-459.67=)-459.670F 0K IN Rankine; [°R] = [K] *9⁄5; 0*9⁄5= 0°R c. The temperature of a system rises by 35°C during a heating process. Express this rise in temperature in Kelvins. For a rise, 1K = 1°C; therefore, a rise of 35°C will be a rise of 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.

For a rise, 1°F = 1°R; therefore, a rise of 80°F will be arise of 80°R For a rise, 1°F=10/18 K; therefore a rise of 80°F will be (5/9)*80= 444/9K or 44.44 K (in 2 d.p) For a rise, 1°F=1°C; therefore a rise of 80°F will be (5/9)*80= 444/9°C or 44.44°C (in 2 d.p) 6) The mass flow rate is 4kg/s, the heat of combustion for C3H8 is 46450kJ/kg. Determine the heat release rate. (1 Mark) Heat release rate = mass flow rate*enthalpy of combustion; 4*46450= 185800 kilowatts 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 states that the rate of heat transfer per unit area normal to the direction of heat flow is directly proportional to the temperature gradient (Nag, 2010). Mathematical expression of Fourier’s law is q = Q/A = -kdT/dx or Q=-kAdT/dx where, q is the heat flux, dT/dx is the thermal gradient in the flow direction, k is thermal conductivity, Q is rate of heat transfer in W, and A is the heat transfer area in m2.

The SI unit of q is watts per meter squared (w/m2) Thermal conductivity is the ability of a substance to conduct heat through it i.e. the rate of heat transfer through a unit thickness of material per unit area per unit temperature difference (Moran and Shapiro 2006). Thermal conductivity of substances is highest in solid phases as compared to gaseous phases. Pure metals have highest thermal conductivity hence they are referred to as good conductors. Most non-metals are poor conductors of heat transfer and thus, they have low values of thermal conductivity.

Therefore, they are called thermal insulators. The minus sign in Fourier's law shows that the heat flows from a hotter point to a colder point.

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