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### Thermodynamics HW Solutions 16

Course: PHY 4803, Fall 2010
School: UNF
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Word Count: 237

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1 Chapter Basics of Heat Transfer 1-37E A copper block and an iron block are dropped into a tank of water. Some heat is lost from the tank to the surroundings during the process. The final equilibrium temperature in the tank is to be determined. Assumptions 1 The water, iron, and copper blocks are incompressible substances with constant specific heats at room temperature. 2 The system is stationary and thus the...

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1 Chapter Basics of Heat Transfer 1-37E A copper block and an iron block are dropped into a tank of water. Some heat is lost from the tank to the surroundings during the process. The final equilibrium temperature in the tank is to be determined. Assumptions 1 The water, iron, and copper blocks are incompressible substances with constant specific heats at room temperature. 2 The system is stationary and thus the kinetic and potential energy changes are zero, KE = PE = 0 and E = U . Properties The specific heats of water, copper, and the iron at room temperature are Cp, water = 1.0 Btu/lbmF, Cp, Copper = 0.092 Btu/lbmF, and Cp, iron = 0.107 Btu/lbmF (Tables A-3E and A-9E). Analysis We take the entire of contents the tank, water + iron + copper blocks, as the system. This is a closed system since no mass crosses the system boundary during the process. The energy balance on the system can be expressed as Ein E out 1 24 43 Net energy transfer by heat, work, and mass = E system 1 24 43 Change in internal, kinetic, potential, etc. energies WATER Qout = U = U copper + U iron + U water or Iron Qout = [mC (T2 T1 )]copper + [mC (T2 T1 )]iron + [mC (T2 T1 )]water Copper Using specific heat values at room temperature for simplicity and substituting, 600Btu = (90lbm)(0.092Btu/lbm F)(T2 160)F + (50lbm)(0.107Btu/lbm F)(T2 200)F + (180lbm)(1.0Btu/lbm F)(T2 70)F T2 = 74.3 F 1-16 600 kJ
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UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-38 A room is heated by an electrical resistance heater placed in a short duct in the room in 15 min whilethe room is losing heat to the outside, and a 200-W fan circulates the air steadily through the heater duct.The
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-39 The resistance heating element of an electrically heated house is placed in a duct. The air is moved bya fan, and heat is lost through the walls of the duct. The power rating of the electric resistance heater is to
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-40 Air is moved through the resistance heaters in a 1200-W hair dryer by a fan. The volume flow rate ofair at the inlet and the velocity of the air at the exit are to be determined.Assumptions 1 Air is an ideal gas si
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-41 The ducts of an air heating system pass through an unheated area, resulting in a temperature drop ofthe air in the duct. The rate of heat loss from the air to the cold environment is to be determined.Assumptions 1
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-42E Air gains heat as it flows through the duct of an air-conditioning system. The velocity of the air atthe duct inlet and the temperature of the air at the exit are to be determined.Assumptions 1 Air is an ideal gas
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-43 Water is heated in an insulated tube by an electric resistance heater. The mass flow rate of waterthrough the heater is to be determined.Assumptions 1 Water is an incompressible substance with a constant specific h
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferHeat Transfer Mechanisms1-44C The thermal conductivity of a material is the rate of heat transfer through a unit thickness of thematerial per unit area and per unit temperature difference. The thermal conductivity of a
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-53C A blackbody is an idealized body which emits the maximum amount of radiation at a giventemperature and which absorbs all the radiation incident on it. Real bodies emit and absorb less radiationthan a blackbody at
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferAssumptions 1 Steady operating conditions exist since the surface temperatures of the wall remainconstant at the specified values. 2 Thermal properties of the wall are constant.Properties The thermal conductivity of the
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-64&quot;GIVEN&quot;&quot;L=0.005 [m], parameter to be varied&quot;A=2*2 &quot;[m^2]&quot;T_1=10 &quot;[C]&quot;T_2=3 &quot;[C]&quot;k=0.78 &quot;[W/m-C]&quot;time=5*3600 &quot;[s]&quot;&quot;ANALYSIS&quot;Q_dot_cond=k*A*(T_1-T_2)/LQ_cond=Q_dot_cond*time*Convert(J, kJ)L [m]0.0010.0020.
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-65 Heat is transferred steadily to boiling water in the pan through its bottom. The inner surface of thebottom of the pan is given. The temperature of the outer surface is to be determined.Assumptions 1 Steady operati
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferAssumptions 1 Steady operating conditions exist since the temperature readings do not change with time.2 Heat losses through the lateral surfaces of the apparatus are negligible since those surfaces are wellinsulated, an
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-69 The thermal conductivity of a material is to be determined by ensuring one-dimensional heatconduction, and by measuring temperatures when steady operating conditions are reached.Assumptions 1 Steady operating condi
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-71 The rate of radiation heat transfer between a person and the surrounding surfaces at specifiedtemperatur es is to be determined in summer and in winter.Assumptions 1 Steady operating conditions exist. 2 Heat transf
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-72&quot;GIVEN&quot;T_infinity=20+273 &quot;[K]&quot;&quot;T_surr_winter=12+273 [K], parameter to be varied&quot;T_surr_summer=23+273 &quot;[K]&quot;A=1.6 &quot;[m^2]&quot;epsilon=0.95T_s=32+273 &quot;[K]&quot;&quot;ANALYSIS&quot;sigma=5.67E-8 &quot;[W/m^2-K^4], Stefan-Boltzman constan
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-73 A person is standing in a room at a specified temperature. The rate of heat transfer between a personand the surrounding air by convection is to be determined.Assumptions 1 Steady operating conditions exist. 2 Heat
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-74 Hot air is blown over a flat surface at a specified temperature. The rate of heat transfer from the air tothe plate is to be determined.Assumptions 1 Steady operating conditions exist. 2 Heat transfer by radiation
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-75&quot;GIVEN&quot;T_infinity=80 &quot;[C]&quot;A=2*4 &quot;[m^2]&quot;T_s=30 &quot;[C]&quot;&quot;h=55 [W/m^2-C], parameter to be varied&quot;&quot;ANALYSIS&quot;Q_dot_conv=h*A*(T_infinity-T_s)h [W/m2.C]2030405060708090100Qconv [W]800012000160002000024000
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-76 The heat generated in the circuitry on the surface of a 3-W silicon chip is conducted to the ceramicsubstrate. The temperature difference across the chip in steady operation is to be determined.Assumptions 1 Steady
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-77 An electric resistance heating element is immersed in water initially at 20C. The time it will take forthis heater to raise the water temperature to 80C as well as the convection heat transfer coefficients at thebe
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-79 A hollow spherical iron container is filled with iced water at 0C. The rate of heat loss from thesphere and the rate at which ice melts in the container are to be determined.Assumptions 1 Steady operating condition
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-80&quot;GIVEN&quot;D=0.2 &quot;[m]&quot;&quot;L=0.4 [cm], parameter to be varied&quot;T_1=0 &quot;[C]&quot;T_2=5 &quot;[C]&quot;&quot;PROPERTIES&quot;h_if=333.7 &quot;[kJ/kg]&quot;k=k_('Iron', 25) &quot;[W/m-C]&quot;&quot;ANALYSIS&quot;A=pi*D^2Q_dot_cond=k*A*(T_2-T_1)/(L*Convert(cm, m)m_dot_ice=(
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-81E The inner and outer glasses of a double pane window with a 0.5-in air space are at specifiedtemperatures. The rate of heat transfer through the window is to be determinedAssumptions 1 Steady operating conditions e
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-82 Two surfaces of a flat plate are maintained at specified temperatures, and the rate of heat transferthrough the plate is measured. The thermal conductivity of the plate material is to be determined.Assumptions 1 St
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-84 A styrofoam ice chest is initially filled with 40 kg of ice at 0C. The time it takes for the ice in thechest to melt completely is to be determined.Assumptions 1 Steady operating conditions exist. 2 The inner and o
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-86&quot;GIVEN&quot;L=0.004 &quot;[m]&quot;D=0.006 &quot;[m]&quot;h=30 &quot;[W/m^2-C]&quot;T_infinity=55 &quot;[C]&quot;&quot;T_case_max=70 [C], parameter to be varied&quot;&quot;ANALYSIS&quot;A=pi*D*L+pi*D^2/4Q_dot=h*A*(T_case_max-T_infinity)Tcase, max [C]6062.56567.57072
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-87E A 200-ft long section of a steam pipe passes through an open space at a specified temperature. Therate of heat loss from the steam pipe and the annual cost of this energy lost are to be determined.Assumptions 1 St
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-89 A 4-m diameter spherical tank filled with liquid oxygen at 1 atm and -183C is exposed toconvection with ambient air. The rate of evaporation of liquid oxygen in the tank as a result of the heattransfer from the amb
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-90&quot;GIVEN&quot;D=4 &quot;[m]&quot;T_s=-196 &quot;[C]&quot;&quot;T_air=20 [C], parameter to be varied&quot;h=25 &quot;[W/m^2-C]&quot;&quot;PROPERTIES&quot;h_fg=198 &quot;[kJ/kg]&quot;&quot;ANALYSIS&quot;A=pi*D^2Q_dot=h*A*(T_air-T_s)m_dot_evap=(Q_dot*Convert(J/s, kJ/s)/h_fgTair [C]0
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-91 A person with a specified surface temperature is subjected to radiation heat transfer in a room atspecified wall temperatures. The rate of radiation heat loss from the person is to be determined.Assumptions 1 Stead
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-92 A circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. All theheat generated in the chips is conducted across the circuit board. The temperature difference between thetwo sides o
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-94 Using the conversion factors between W and Btu/h, m and ft, and K and R, the Stefan-Boltzmannconstant = 5.67 108 W / m2 . K4 is to be expressed in the English unit, Btu / h. ft 2 . R 4 .Analysis The conversion fact
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferSimultaneous Heat Transfer Mechanisms1-96C All three modes of heat transfer can not occur simultaneously in a medium. A medium may involvetwo of them simultaneously.1-97C (a) Conduction and convection: No. (b) Conducti
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-101 Two large plates at specified temperatures are held parallel to each other. The rate of heat transferbetween the plates is to be determined for the cases of still air, regular insulation, and super insulationbetwe
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-102 The convection heat transfer coefficient for heat transfer from an electrically heated wire to air is tobe determined by measuring temperatures when steady operating conditions are reached and the electricpower co
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-103&quot;GIVEN&quot;L=1.4 &quot;[m]&quot;D=0.002 &quot;[m]&quot;T_infinity=20 &quot;[C]&quot;&quot;T_s=240 [C], parameter to be varied&quot;V=110 &quot;[Volt]&quot;I=3 &quot;[Ampere]&quot;&quot;ANALYSIS&quot;Q_dot=V*IA=pi*D*LQ_dot=h*A*(T_s-T_infinity)Ts [C]1001201401601802002202
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-104E A spherical ball whose surface is maintained at a temperature of 170F is suspended in the middleof a room at 70F. The total rate of heat transfer from the ball is to be determined.Assumptions 1 Steady operating c
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-105 A 1000-W iron is left on the iron board with its base exposed to the air at 20C. The temperature ofthe base of the iron is to be determined in steady operation.Assumptions 1 Steady operating conditions exist. 2 Th
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-107 A spherical tank located outdoors is used to store iced water at 0C. The rate of heat transfer to theiced water in the tank and the amount of ice at 0 C that melts during a 24-h period are to be determined.Assumpt
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-108 The roof of a house with a gas furnace consists of a 15-cm thick concrete that is losing heat to theoutdoors by radiation and convection. The rate of heat transfer through the roof and the money lostthrough the ro
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-109E A flat plate solar collector is placed horizontally on the roof of a house. The rate of heat loss fromthe collector by convection and radiation during a calm day are to be determined.Assumptions 1 Steady operatin
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferProblem Solving Techniques and EES1-110C Despite the convenience and capability the engineering software packages offer, they are still justtools, and they will not replace the traditional engineering courses. They will
UNF - PHY - 4803
Chapter 1 Basics of Heat Transfer1-113 Solve the following system of 3 equations with 3 unknowns using EES:2x y + z = 53x2 + 2y = z + 2xy + 2z = 8Solution by EES Software (Copy the following lines and paste on a blank EES screen to verifysolution):
UNF - PHY - 4803
Chapter 1 Basics of Heat TransferSpecial Topic: Thermal Comfort1-115C The metabolism refers to the burning of foods such as carbohydrates, fat, and protein in order toperform the necessary bodily functions. The metabolic rate for an average man ranges
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