Energy Transfer and Thermodynamics - Assignment Example

1. Define the four laws of thermodynamics using words, diagrams and equations where appropriate. (6 Marks) Zeroth law of thermodynamics states that “suppose there exist three systems A, B and C. If system A is in thermal equilibrium with system B and also in thermal equilibrium with system C, then the system B should be in thermal equilibrium with system C independently” (Arora, 2011 p. 49). Diathermal wall (a) (b) Adiabatic wall 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 Kothandaraman and Subramanyan (2008), the second law of thermodynamics states that “the flow of energy as heat through a system boundary will always be in the direction of lower temperature or along the negative temperature gradient” (p. 2). 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” (Rao, 2004, p. 210). 2. What is entropy? Explain why liquids are more disordered than solids and why gases are more disordered than liquids? (2 Marks) According to Moran and Shapiro (2006), entropy, S, refers to the measure of disorder of a system. As a solid substance absorbs heat energy, it increases the kinetic energy of its molecules changing its state to liquid. Similarly, the liquids change to gaseous state. The increase in kinetic energy increases the entropy of the system and thus making liquids more disordered than solids and gases more disordered than liquids. 3. Predict whether entropy increases or decrease for the following reaction and explain why. (Do not calculate entropy): CaCO3(s) → CaO(s) + CO2(g) - Entropy increases N2(g) + 3H2(g) ↔2NH3(g) - Entropy decreases NH4NO3(s) → NH4+(aq) + NO3¯(aq) - Entropy increases H2O(g) ↔ H2O(l) - Entropy decreases (4 Marks) 4. Calculate ΔS for the following reaction, using the thermodynamic data provided. (8 Marks). Substances                S0 (J/K.mol) NaCl(s) 72 NaCl(aq) 57 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 NO2 240 ΔS0reaction = ΣnpS0 (products) – ΣnrS0 (reactants); where np represents the number of moles of each product and nr represent the moles of each reactant. a. NaCl(s) → Na+ (aq) + Cl¯ (aq) ∆S0 = [116-72] = 44 J/K b. 2NO (g) +O2 (g) → N2O4 (g) ∆S0 = [304]-[(2*211) +205] = -321 J/K c. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (l). ∆S0 = [214+ (70*2]-[186+ (205*2)] = -242 J/K d. 2NO2 (g) ↔ N2O4 (g) ∆S0 = [304]-[2*240] = -176 J/K 5. These questions test your understanding of temperature measurements and temperature scales. (6 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 45°C during a heating process. Express this rise in temperature in Kelvins. For a rise, 1K = 1°C; therefore, a rise of 45°C will be a rise of 45K d. The temperature of a system rises by 180°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 180°F will be arise of 180°R For a rise, 1°F=5/9 K; therefore a rise of 180°F will be (5/9)*180= 100K For a rise, 1°F =5/9K=5/9°C; therefore a rise of 180°F will be (5/9)*180= 100°C 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 Fouriers Law defining all the terms used within it. 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? (8 Marks) According to Nag (2010), 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. This can be mathematically expressed as 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) Moran and Shapiro (2006) defines thermal conductivity as 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. Substances in solid phases have high thermal conductivity than those in gaseous phases. Thermal conductivity is highest in pure metals and thus 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 are the ranges 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? (8 Marks Stefen-Boltzman Law states that the radiating heat flux or emmissive radiations is proportional to the fourth power of temperature on absolute scale (Moran and Shapiro, 2006). 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). Emissivity is the ratio 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. (8 Marks) Heat of combustion is the heat given when one mole of the substance undergoes a complete combustion with oxygen at constant pressure. Heat release rate refers to the amount of heat released by a burning substance and is recorded in Kw (Kothandaraman and Subramanyan, 2008). The total heat release rate is obtained by adding the contributions from each part of the burning area and the burner. Q total =Q product +Q burner Combustion reaction refers to a chemical reaction that 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 it a good absorber of radiation, a good emitter or a poor emitter? (2 Marks) E b=σT4; E = 5.669×10-8 W/m2K4 *(20+273) K4 =4.18X102W/m2. It is a good emitter of radiation. 11. Explain Newton’s Law of cooling and give the mathematical equation defining all the terms used. How is natural convection different from forced convection? (4 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. 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 (Shang, 2010). On the other hand (in forced convection), the fluid is forced to flow over a solid surface by external means such as a pump or a fan. 12. Aluminum has a specific heat of 0.902 J/g0C.   How much heat is lost when a piece of aluminum with a mass of 28.984 g cools from a temperature of 615.0oC to a temperature of 122.0oC? (2 Marks) q = m * Cg *(Tf - Ti) q = 28.984g*0.902 J/g0C*(122-615) 0C; 28.984*0.902*-493 = -12888.78J Therefore, the amount of heat lost is 12888.78J 13. 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% 14. The temperature of a sample of water increases by 39.5oC when 24 500 J are applied.  The specific heat of liquid water is 4.18 J/goC.  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 *39.5 oC; 24500/ (4.18*39.5) = 148.39g 15. How much energy does it take to raise the temperature of 80 g of copper by 30 °C? Specific heat of copper is 0.385 J/g ºC. (2 Marks) q = m * Cg * (Tf - Ti); q =80g*0.385 J/g ºC*30°C = 924J 16. Define the following terms: (4 Marks) a. Heat capacity, CP, is the amount of heat required to raise the temperature of a substance by 1K. b. Specific heat, Specific heat, Q, is the amount of heat per unit mass required to raise the temperature by 10C c. Isothermal process refers to a change in a system at a constant temperature (T= Constant, ΔT = 0). d. Isobaric process, is a process in which the pressure remains constant (p = constant, ΔP=0). e. Isochoric process is a process that takes place at the constant volume (V = Constant, dV = 0). 17. Heat is added to a system, and the system does 56 J of work. If the internal energy increases by 17J, 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, 17J = q + -56J; 17+56 =73J. 18. A 60kg block of iron is heated from 20°C to 125°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* (125-20) 0C *0.45J/g0C = 2835000J or 2835Kj. 19. 150J of heat are injected into a heat engine, causing it to do work. The engine then exhausts 45J of heat into a cool reservoir. What is the efficiency of the engine? (2 Marks) Efficiency = Work output / Work input x 100%; efficiency =45/150*100% = 30% 20. What is kinetic energy and how does it relate to the temperature of a system? (2 Marks) Kinetic energy is the amount of energy that a substance posses due to its motion. This amount of energy leads to a rise in the temperature of a system. 21. 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. (6 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 22. Gold has a specific heat of 0.129 J/g °C. If 15.0 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=15g* Δt*0.129J/g °C; Δt= 1.33/1.935= 0.690C 23. A gas absorbs 3.5J of heat and then performs 1.5J of work. What is the change in internal energy of the gas? (2 Marks) ΔE = q + w; we take w to be negative since it is the gas that does the work; ΔE = 3.5J +-1.5J = 2J 24. 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. Mathematically, it can be expressed as 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). 25. Explain what intensive and extensive properties are, giving examples of each to support your answer. (1 Mark) Kaviany (2002) defines intensive properties as the thermodynamic properties which are independent of the amount of mass present. Examples include pressure, temperature and density. On the other hand, extensive properties refer to the thermodynamic properties which depend on the amount of mass present. Examples include mass, total volume and weight. 26. Discus the different types of systems encountered in thermodynamics. What is the state postulate? (3 Marks) There are three types of systems encountered in thermodynamics; open, closed and isolated (Kaviany 2002). 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. State postulate states that “for a given thermodynamic system, the number of independently variable thermodynamic properties to be specified for specifying the state of a system is equal to the number of work modes plus one” (Rao, 2004 p.44 ). 27. A can of soft drink at room temperature is put into the refrigerator so that it will cool. Would you model the can of soft drink as a closed system or as an open system? Explain. (2 Marks) This is a closed system because it is only the energy that changes, but its mass remains constant. 28. For a system to be in thermodynamic equilibrium, do the temperature and the pressure have to be the same everywhere? (1 Mark) Yes. For the temperature, it is a requirement that it remains uniform throughout the system. Another requirement for thermodynamic equilibrium is that there must be no unbalanced forces between parts of the system (Moran, Shapiro, Boettner and Bailey, 2010). 29. What is a quasi-equilibrium process? What is its importance in engineering? (2 Marks) This is a process in which the departure from thermodynamic equilibrium is at most infinitesimal (Moran, Shapiro, Boettner and Bailey 2010, p. 47). Quai-equilibrium serves as standards to which actual processes can be compared. The concept is actually instrumental in deducing relationships that exist among the properties of systems at equilibrium. 30. Consider two closed systems A and B. System A contains 3000 kJ of thermal energy at 20°C, whereas system B contains 200 kJ of thermal energy at 50°C. Now the systems are brought into contact with each other. Determine the direction of any heat transfer between the two systems (2 Marks). Since the two systems are in contact with one another and there is no flow of mass, heat transfer between these systems will be through conduction. According to the second law of thermodynamics, heat will, therefore, be transferred from system B to system A (i.e in the direction of lower temperature). List of references Arora, CP 2011. Thermodynamics. Delhi: Tata McGraw-Hill Education. Balmer, RT 2010. Modern Engineering Thermodynamics. Massachusetts: Academic Press. Kaviany, M 2002. Principles of heat transfer. Great Britain: Wiley-IEEE. Kothandaraman, CP and Subramanyan, S 2008. Fundamentals of heat and mass transfer, 3rd edn. New Jersey, NJ: New Age International. Moran, MJ and Shapiro, HN 2006. Fundamentals of engineering thermodynamics, 5th edn. New York, NY: John Wiley and Sons. Nag, H 2010. Basic & Applied Thermodynamics, 2nd edn. New Delhi: Tata McGraw-Hill Education. Rao, C 2004. An introduction to thermodynamics. New York, NY: Universities Press. Rathore, R and Kapuno N 2010. Engineering heat transfer, 2nd edn. Canada: Jones & Bartlett Learning. Shang, D 2010. Theory of Heat Transfer with Forced Convection Film Flows. Canada: Springer. Read More

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. (8 Marks) Heat of combustion is the heat given when one mole of the substance undergoes a complete combustion with oxygen at constant pressure.

Heat release rate refers to the amount of heat released by a burning substance and is recorded in Kw (Kothandaraman and Subramanyan, 2008). The total heat release rate is obtained by adding the contributions from each part of the burning area and the burner. Q total =Q product +Q burner Combustion reaction refers to a chemical reaction that 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 it a good absorber of radiation, a good emitter or a poor emitter? (2 Marks) E b=σT4; E = 5.669×10-8 W/m2K4 *(20+273) K4 =4.18X102W/m2. It is a good emitter of radiation. 11. Explain Newton’s Law of cooling and give the mathematical equation defining all the terms used. How is natural convection different from forced convection? (4 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. 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 (Shang, 2010). On the other hand (in forced convection), the fluid is forced to flow over a solid surface by external means such as a pump or a fan. 12. Aluminum has a specific heat of 0.902 J/g0C.   How much heat is lost when a piece of aluminum with a mass of 28.

984 g cools from a temperature of 615.0oC to a temperature of 122.0oC? (2 Marks) q = m * Cg *(Tf - Ti) q = 28.984g*0.902 J/g0C*(122-615) 0C; 28.984*0.902*-493 = -12888.78J Therefore, the amount of heat lost is 12888.78J 13. 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.

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