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### Thermodynamics HW Solutions 60

Course: PHY 4803, Fall 2010
School: UNF
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Word Count: 518

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1 Chapter Basics of Heat Transfer Special Topic: Thermal Comfort 1-115C The metabolism refers to the burning of foods such as carbohydrates, fat, and protein in order to perform the necessary bodily functions. The metabolic rate for an average man ranges from 108 W while reading, writing, typing, or listening to a lecture in a classroom in a seated position to 1250 W at age 20 (730 at age 70) during strenuous...

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1 Chapter Basics of Heat Transfer Special Topic: Thermal Comfort 1-115C The metabolism refers to the burning of foods such as carbohydrates, fat, and protein in order to perform the necessary bodily functions. The metabolic rate for an average man ranges from 108 W while reading, writing, typing, or listening to a lecture in a classroom in a seated position to 1250 W at age 20 (730 at age 70) during strenuous exercise. The corresponding rates for women are about 30 percent lower. Maximum metabolic rates of trained athletes can exceed 2000 W. We are interested in metabolic rate of the occupants of a building when we deal with heating and air conditioning because the metabolic rate represents the rate at which a body generates heat and dissipates it to the room. This body heat contributes to the heating in winter, but it adds to the cooling load of the building in summer. 1-116C The metabolic rate is proportional to the size of the body, and the metabolic rate of women, in general, is lower than that of men because of their smaller size. Clothing serves as insulation, and the thicker the clothing, the lower the environmental temperature that feels comfortable. 1-117C Asymmetric thermal radiation is caused by the cold surfaces of large windows, uninsulated walls, or cold products on one side, and the warm surfaces of gas or electric radiant heating panels on the walls or ceiling, solar heated masonry walls or ceilings on the other. Asymmetric radiation causes discomfort by exposing different sides of the body to surfaces at different and temperatures thus to different rates of heat loss or gain by radiation. A person whose left side is exposed to a cold window, for example, will feel like heat is being drained from that side of his or her body. 1-118C (a) Draft causes undesired local cooling of the human body by exposing parts of the body to high heat transfer coefficients. (b) Direct contact with cold floor surfaces causes localized discomfort in the feet by excessive heat loss by conduction, dropping the temperature of the bottom of the feet to uncomfortable levels. 1-119C Stratification is the formation of vertical still air layers in a room at difference temperatures, with highest temperatures occurring near the ceiling. It is likely to occur at places with high ceilings. It causes discomfort by exposing the head and the feet to different temperatures. This effect can be prevented or minimized by using destratification fans (ceiling fans running in reverse). 1-120C It is necessary to ventilate buildings to provide adequate fresh air and to get rid of excess carbon dioxide, contaminants, odors, and humidity. Ventilation increases the energy consumption for heating in winter by replacing the warm indoors air by the colder outdoors air. Ventilation also increases the energy consumption for cooling in summer by replacing the cold indoors air by the warm outdoors air. It is not a good idea to keep the bathroom fans on all the time since they will waste energy by expelling conditioned air (warm in winter and cool in summer) by the unconditioned outdoor air. 1-60
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UNF - PHY - 4803
Chapter 1 Basics of Heat TransferReview Problems1-121 Cold water is to be heated in a 1200-W teapot. The time needed to heat the water is to bedetermined.Assumptions 1 Steady operating conditions exist. 2 Thermal properties of the teapot and the water
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-122 The duct of an air heating system of a house passes through an unheated space in the attic. The rateof heat loss from the air in the duct to the attic and its cost under steady conditions are to be determined.Assu
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-123&quot;GIVEN&quot;L=4 &quot;[m]&quot;D=0.2 &quot;[m]&quot;P_air_in=100 &quot;[kPa]&quot;T_air_in=65 &quot;[C]&quot;&quot;Vel=3 [m/s], parameter to be varied&quot;T_air_out=60 &quot;[C]&quot;eta_furnace=0.82Cost_gas=0.58 &quot;[\$/therm]&quot;&quot;PROPERTIES&quot;R=0.287 &quot;[kJ/kg-K], gas constant
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-124 Water is heated from 16C to 43C by an electric resistance heater placed in the water pipe as itflows through a showerhead steadily at a rate of 10 L/min. The electric power input to the heater, and themoney that w
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-125 Water is to be heated steadily from 15C to 50C by an electrical resistor inside an insulated pipe.The power rating of the resistance heater and the average velocity of the water are to be determined.Assumptions 1
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-126 The heating of a passive solar house at night is to be assisted by solar heated water. The length oftime that the electric heating system would run that night with or without solar heating are to bedetermined.Ass
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-127 A standing man is subjected to high winds and thus high convection coefficients. The rate of heatloss from this man by convection in still air at 20C, in windy air, and the wind-chill factor are to bedetermined.A
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-129 A room is to be heated by 1 ton of hot water contained in a tank placed in the room. The minimuminitial temperature of the water is to be determined if it to meet the heating requirements of this room for a24-h pe
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-131 A refrigerator consumes 600 W of power when operating, and its motor remains on for 5 min andthen off for 15 min periodically. The average thermal conductivity of the refrigerator walls and the annualcost of opera
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-132 A 0.2-L glass of water at 20C is to be cooled with ice to 5C. The amounts of ice or cold water thatneeds to be added to the water are to be determined.Assumptions 1 Thermal properties of the ice and water are cons
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-133&quot;GIVEN&quot;V=0.0002 &quot;[m^3]&quot;T_w1=20 &quot;[C]&quot;T_w2=5 &quot;[C]&quot;&quot;T_ice=0 [C], parameter to be varied&quot;T_melting=0 &quot;[C]&quot;&quot;PROPERTIES&quot;rho=density(water, T=25, P=101.3) &quot;at room temperature&quot;C_w=CP(water, T=25, P=101.3) &quot;at room
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-134E A 1-short ton (2000 lbm) of water at 70F is to be cooled in a tank by pouring 160 lbm of ice at25F into it. The final equilibrium temperature in the tank is to be determined. The melting temperature andthe heat o
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-136 Somebody takes a shower using a mixture of hot and cold water. The mass flow rate of hot waterand the average temperature of mixed water are to be determined.Assumptions The hot water temperature changes from 80C
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-137 The glass cover of a flat plate solar collector with specified inner and outer surface temperatures isconsidered. The fraction of heat lost from the glass cover by radiation is to be determined.Assumptions 1 Stead
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-138 The range of U-factors for windows are given. The range for the rate of heat loss through thewindow of a house is to be determined.Assumptions 1 Steady operating conditions exist. 2 Heat losses associated with the
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-139&quot;GIVEN&quot;A=1.2*1.8 &quot;[m^2]&quot;T_1=20 &quot;[C]&quot;T_2=-8 &quot;[C]&quot;&quot;U=1.25 [W/m^2-C], parameter to be varied&quot;&quot;ANALYSIS&quot;Q_dot_window=U*A*(T_1-T_2)U [W/m2.C]1.251.752.252.753.253.754.254.755.255.756.25Qwindow [W]75.6
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-140 . . . 1-144 Design and Essay Problems1-77
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationChapter 2HEAT CONDUCTION EQUATIONIntroduction2-1C Heat transfer is a vector quantity since it has direction as well as magnitude. Therefore, we mustspecify both direction and magnitude in order to describe heat trans
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-6C Heat transfer to a hot dog can be modeled as two-dimensional since temperature differences (and thusheat transfer) will exist in the radial and axial directions (but there will be symmetry about the center lineand
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation&amp;g=&amp;GV wire=&amp;G(D / 4) L2= 3.412 Btu/h 73 = 7.820 10 Btu/h ft1W[(0.08 / 12 ft) / 4](15 / 12 ft) 1000 W2Similarly, heat flux on the outer surface of the wire as a result of this heat generation is determ
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-15E&quot;GIVEN&quot;E_dot=1000 &quot;[W]&quot;L=15 &quot;[in]&quot;&quot;D=0.08 [in], parameter to be varied&quot;&quot;ANALYSIS&quot;g_dot=E_dot/V_wire*Convert(W, Btu/h)V_wire=pi*D^2/4*L*Convert(in^3, ft^3)q_dot=E_dot/A_wire*Convert(W, Btu/h)A_wire=pi*D*L*Co
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-16 The rate of heat generation per unit volume in the uranium rods is given. The total rate of heatgeneration in each rod is to be determined.g = 7107 W/m3Assumptions Heat is generated uniformly in the uranium rods.
UNF - PHY - 4803
Chapter 2 Heat Conduction Equationvariable, g is the heat generation per unit volume, k is the thermal conductivity, is the thermal diffusivity,and t is the time.2-6
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-21 We consider a thin element of thickness x in a large plane wall (see Fig. 2-13 in the text). Thedensity of the wall is , the specific heat is C, and the area of the wall normal to the direction of heattransfer is
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-22 We consider a thin cylindrical shell element of thickness r in a long cylinder (see Fig. 2-15 in thetext). The density of the cylinder is , the specific heat is C, and the length is L. The area of the cylindernorm
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-23 We consider a thin spherical shell element of thickness r in a sphere (see Fig. 2-17 in the text). Thedensity of the sphere is , the specific heat is C, and the length is L. The area of the sphere normal to thedir
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation(a) Heat transfer is transient, (b) it is one-dimensional, (c) there is no heat generation, and (d) the thermalconductivity is constant.2-27 For a medium in which the heat conduction equation is given in its simplest b
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-29 We consider a thin ring shaped volume element of width z and thickness r in a cylinder. Thedensity of the cylinder is and the specific heat is C. In general, an energy balance on this ring elementduring a small ti
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-30 Consider a thin disk element of thickness z and diameter D in a long cylinder (Fig. P2-30). Thedensity of the cylinder is , the specific heat is C, and the area of the cylinder normal to the direction ofheat trans
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-31 For a medium in which the heat conduction equation is given by2Tx2+2Ty2=1 T: t(a) Heat transfer is transient, (b) it is two-dimensional, (c) there is no heat generation, and (d) the thermalconductivity
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-39C We try to avoid the radiation boundary condition in heat transfer analysis because it is a non-linearexpression that causes mathematical difficulties while solving the problem; often making it impossible toobtain
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-43 A spherical shell of inner radius r1 , outer radius r2 , and thermal conductivity k is considered. Theouter surface of the shell is subjected to radiation to surrounding surfaces at Tsurr . Assuming no convectiona
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-46E A 1.5-kW resistance heater wire is used for space heating. Assuming constant thermal conductivityand one-dimensional heat transfer, the mathematical formulation (the differential equation and theboundary conditio
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-48 Water flows through a pipe whose outer surface is wrapped with a thin electric heater that consumes300 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that the entireheat gene
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationAssumptions 1 Heat transfer is given to be transient and one-dimensional. 2 Thermal conductivity is givento be variable. 3 There is no heat generation in the medium. 4 The outer surface at r = r0 is subjected toconvect
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationSolution of Steady One-Dimensional Heat Conduction Problems2-52C Yes, this claim is reasonable since in the absence of any heat generation the rate of heat transferthrough a plain wall in steady operation must be const
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-56 A large plane wall is subjected to specified temperature on the left surface and convection on the rightsurface. The mathematical formulation, the variation of temperature, and the rate of heat transfer are to bed
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-57 The top and bottom surfaces of a solid cylindrical rod are maintained at constant temperatures of20C and 95C while the side surface is perfectly insulated. The rate of heat transfer through the rod is tobe determi
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-58&quot;GIVEN&quot;L=0.15 &quot;[m]&quot;D=0.05 &quot;[m]&quot;T_1=20 &quot;[C]&quot;T_2=95 &quot;[C]&quot;&quot;k=1.2 [W/m-C], parameter to be varied&quot;&quot;ANALYSIS&quot;A=pi*D^2/4Q_dot=k*A*(T_2-T_1)/Lk [W/m.C]122436485106127148169190211232253274295316337
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-59 The base plate of a household iron is subjected to specified heat flux on the left surface and tospecified temperature on the right surface. The mathematical formulation, the variation of temperature inthe plate,
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-60 The base plate of a household iron is subjected to specified heat flux on the left surface and tospecified temperature on the right surface. The mathematical formulation, the variation of temperature inthe plate,
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-61&quot;GIVEN&quot;Q_dot=800 &quot;[W]&quot;L=0.006 &quot;[m]&quot;A_base=160E-4 &quot;[m^2]&quot;k=20 &quot;[W/m-C]&quot;T_2=85 &quot;[C]&quot;&quot;ANALYSIS&quot;q_dot_0=Q_dot/A_baseT=q_dot_0*(L-x)/k+T_2 &quot;Variation of temperature&quot;&quot;x is the parameter to be varied&quot;00.0006667
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationAssumptions 1 Heat conduction is steady and one-dimensional since the pipe is long relative to itsthickness, and there is thermal symmetry about the center line. 2 Thermal conductivity is constant. 3 Thereis no heat ge
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-27
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-63 A spherical container is subjected to specified temperature on the inner surface and convection on theouter surface. The mathematical formulation, the variation of temperature, and the rate of heat transfer areto
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationC1r (T T )dT&amp;= k (4r 2 ) 2 = 4kC1 = 4k 2 1 Q = kArkdxr1 2 r1 hr2(2.1 m)(0 25)C= 4 (30 W/m C)= 23,460 W2.130 W/m C12 (18 W/m 2 C)(2.1 m )2-29
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-64 A large plane wall is subjected to specified heat flux and temperature on the left surface and noconditions on the right surface. The mathematical formulation, the variation of temperature in the plate,and the rig
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-65 A large plane wall is subjected to specified heat flux and temperature on the left surface and noconditions on the right surface. The mathematical formulation, the variation of temperature in the plate,and the rig
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-66E A large plate is subjected to convection, radiation, and specified temperature on the top surface andno conditions on the bottom surface. The mathematical formulation, the variation of temperature in theplate, an
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-67E A large plate is subjected to convection and specified temperature on the top surface and noconditions on the bottom surface. The mathematical formulation, the variation of temperature in the plate,and the bottom
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-68 A compressed air pipe is subjected to uniform heat flux on the outer surface and convection on theinner surface. The mathematical formulation, the variation of temperature in the pipe, and the surfacetemperatures
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation(c) The inner and outer surface temperatures are determined by direct substitution to berInner surface (r = r1): T (r1 ) = 10 + 0.483 ln 1 + 12.61 = 10 + 0.483(0 + 12.61) = 3.91Cr1r 0.04Outer surface (r = r2): T (
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-69&quot;GIVEN&quot;L=6 &quot;[m]&quot;r_1=0.037 &quot;[m]&quot;r_2=0.04 &quot;[m]&quot;k=14 &quot;[W/m-C]&quot;Q_dot=300 &quot;[W]&quot;T_infinity=-10 &quot;[C]&quot;h=30 &quot;[W/m^2-C]&quot;f_loss=0.15&quot;ANALYSIS&quot;q_dot_s=(1-f_loss)*Q_dot)/AA=2*pi*r_2*LT=T_infinity+(ln(r/r_1)+k/(h*r_1)
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationAssumptions 1 Heat conduction is steady and one-dimensional since there is no change with time andthere is thermal symmetry about the mid point. 2 Thermal conductivity is constant. 3 There is no heatgeneration in the c
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation&amp;&amp;Q = mC p T m =&amp;Q0.450 kJ / s== 0.00134 kg / s = 4.84 kg / hC p T (4.185 kJ / kg C)(100 20) C2-38
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-71&quot;GIVEN&quot;r_1=0.40 &quot;[m]&quot;r_2=0.41 &quot;[m]&quot;k=1.5 &quot;[W/m-C]&quot;T_1=100 &quot;[C]&quot;Q_dot=500 &quot;[W]&quot;f_loss=0.10&quot;ANALYSIS&quot;q_dot_s=(1-f_loss)*Q_dot)/AA=4*pi*r_2^2T=T_1+(1/r_1-1/r)*(q_dot_s*r_2^2)/k &quot;Variation of temperature&quot;&quot;r i
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationHeat Generation in Solids2-72C No. Heat generation in a solid is simply the conversion of some form of energy into sensible heatenergy. For example resistance heating in wires is conversion of electrical energy to heat
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-78 Heat is generated in a long solid cylinder with a specified surfacetemperature. The variation of temperature in the cylinder is given byT (r ) =2&amp;gr02 r 1 + Tsk r0 80C(a) Heat conduction is steady since t
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-79&quot;GIVEN&quot;r_0=0.04 &quot;[m]&quot;k=25 &quot;[W/m-C]&quot;g_dot_0=35E+6 &quot;[W/m^3]&quot;T_s=80 &quot;[C]&quot;&quot;ANALYSIS&quot;T=(g_dot_0*r_0^2)/k*(1-(r/r_0)^2)+T_s &quot;Variation of temperature&quot;&quot;r is the parameter to be varied&quot;r [m]00.0044440.0088890.01
UNF - PHY - 4803
Chapter 2 Heat Conduction Equation2-80E A long homogeneous resistance heater wire with specified convection conditions at the surface isused to boil water. The mathematical formulation, the variation of temperature in the wire, and thetemperature at th
UNF - PHY - 4803
Chapter 2 Heat Conduction EquationT ( 0) = T +&amp;&amp;g 2 gr0r0 +4k2h2= 212F +(1800 Btu/h.in 3 )(0.25 in) 2 12 in (1800 Btu/h.in 3 )(0.25 in ) 12 in + = 290.8F4 (8.6 Btu/h.ft.F)2 (820 Btu/h ft 2 F) 1 ft 1 ft Thus the centerline temperature will