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Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 8.8, Problem 80P
a)
To determine
The rate of heat transfer
b)
To determine
The exergy destroyed during the process
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The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
Chapter 8 Solutions
Thermodynamics: An Engineering Approach
Ch. 8.8 - What final state will maximize the work output of...Ch. 8.8 - Is the exergy of a system different in different...Ch. 8.8 - How does useful work differ from actual work? For...Ch. 8.8 - Prob. 4PCh. 8.8 - Consider two geothermal wells whose energy...Ch. 8.8 - Consider two systems that are at the same pressure...Ch. 8.8 - Prob. 7PCh. 8.8 - Does a power plant that has a higher thermal...Ch. 8.8 - Prob. 9PCh. 8.8 - 8–10C Can a process for which the reversible work...
Ch. 8.8 - 8–11C Consider a process during which no entropy...Ch. 8.8 - Prob. 12PCh. 8.8 - 8–13E Saturated stem is generated in a boiler by...Ch. 8.8 - One method of meeting the extra electric power...Ch. 8.8 - Prob. 15PCh. 8.8 - A heat engine that receives heat from a furnace at...Ch. 8.8 - Consider a thermal energy reservoir at 1500 K that...Ch. 8.8 - A heat engine receives heat from a source at 1100...Ch. 8.8 - A heat engine that rejects waste heat to a sink at...Ch. 8.8 - Prob. 21PCh. 8.8 - A freezer is maintained at 20F by removing heat...Ch. 8.8 - Prob. 23PCh. 8.8 - Can a system have a higher second-law efficiency...Ch. 8.8 - A mass of 8 kg of helium undergoes a process from...Ch. 8.8 - Prob. 26PCh. 8.8 - Which is a more valuable resource for work...Ch. 8.8 - Which has the capability to produce the most work...Ch. 8.8 - A pistoncylinder device contains 8 kg of...Ch. 8.8 - The radiator of a steam heating system has a...Ch. 8.8 - A well-insulated rigid tank contains 6 lbm of a...Ch. 8.8 - Prob. 33PCh. 8.8 - Prob. 35PCh. 8.8 - Prob. 36PCh. 8.8 - A pistoncylinder device initially contains 2 L of...Ch. 8.8 - A 0.8-m3 insulated rigid tank contains 1.54 kg of...Ch. 8.8 - An insulated pistoncylinder device initially...Ch. 8.8 - An insulated rigid tank is divided into two equal...Ch. 8.8 - Prob. 41PCh. 8.8 - Prob. 42PCh. 8.8 - Prob. 43PCh. 8.8 - Prob. 44PCh. 8.8 - Prob. 45PCh. 8.8 - Prob. 46PCh. 8.8 - A pistoncylinder device initially contains 1.4 kg...Ch. 8.8 - Prob. 48PCh. 8.8 - Prob. 50PCh. 8.8 - Prob. 51PCh. 8.8 - Air enters a nozzle steadily at 200 kPa and 65C...Ch. 8.8 - Prob. 55PCh. 8.8 - Prob. 56PCh. 8.8 - Argon gas enters an adiabatic compressor at 120...Ch. 8.8 - Prob. 58PCh. 8.8 - Prob. 59PCh. 8.8 - Prob. 60PCh. 8.8 - Combustion gases enter a gas turbine at 900C, 800...Ch. 8.8 - Prob. 62PCh. 8.8 - Refrigerant-134a is condensed in a refrigeration...Ch. 8.8 - Prob. 64PCh. 8.8 - Refrigerant-22 absorbs heat from a cooled space at...Ch. 8.8 - Prob. 66PCh. 8.8 - Prob. 67PCh. 8.8 - Prob. 68PCh. 8.8 - Prob. 69PCh. 8.8 - Air enters a compressor at ambient conditions of...Ch. 8.8 - Hot combustion gases enter the nozzle of a...Ch. 8.8 - Prob. 72PCh. 8.8 - Prob. 73PCh. 8.8 - Prob. 74PCh. 8.8 - Prob. 75PCh. 8.8 - Prob. 76PCh. 8.8 - Prob. 77PCh. 8.8 - An insulated vertical pistoncylinder device...Ch. 8.8 - Prob. 79PCh. 8.8 - Prob. 80PCh. 8.8 - Prob. 81PCh. 8.8 - Steam is to be condensed on the shell side of a...Ch. 8.8 - 8–83 Air enters a compressor at ambient conditions...Ch. 8.8 - Prob. 84PCh. 8.8 - Prob. 85PCh. 8.8 - Prob. 86RPCh. 8.8 - Prob. 87RPCh. 8.8 - Steam enters an adiabatic nozzle at 3.5 MPa and...Ch. 8.8 - Prob. 89RPCh. 8.8 - Prob. 91RPCh. 8.8 - A well-insulated, thin-walled, counterflow heat...Ch. 8.8 - Prob. 93RPCh. 8.8 - Prob. 94RPCh. 8.8 - Prob. 95RPCh. 8.8 - Prob. 96RPCh. 8.8 - Prob. 97RPCh. 8.8 - Prob. 98RPCh. 8.8 - Prob. 99RPCh. 8.8 - Prob. 100RPCh. 8.8 - Prob. 101RPCh. 8.8 - A pistoncylinder device initially contains 8 ft3...Ch. 8.8 - Steam at 7 MPa and 400C enters a two-stage...Ch. 8.8 - Steam enters a two-stage adiabatic turbine at 8...Ch. 8.8 - Prob. 105RPCh. 8.8 - Prob. 106RPCh. 8.8 - Prob. 107RPCh. 8.8 - Prob. 108RPCh. 8.8 - Prob. 109RPCh. 8.8 - Prob. 111RPCh. 8.8 - Prob. 112RPCh. 8.8 - A passive solar house that was losing heat to the...Ch. 8.8 - Prob. 114RPCh. 8.8 - Prob. 115RPCh. 8.8 - Prob. 116RPCh. 8.8 - Prob. 117RPCh. 8.8 - Prob. 118RPCh. 8.8 - A 4-L pressure cooker has an operating pressure of...Ch. 8.8 - Repeat Prob. 8114 if heat were supplied to the...Ch. 8.8 - Prob. 121RPCh. 8.8 - Prob. 122RPCh. 8.8 - Reconsider Prob. 8-120. The air stored in the tank...Ch. 8.8 - Prob. 124RPCh. 8.8 - Prob. 125RPCh. 8.8 - Prob. 126RPCh. 8.8 - Prob. 127RPCh. 8.8 - Prob. 128RPCh. 8.8 - Water enters a pump at 100 kPa and 30C at a rate...Ch. 8.8 - Prob. 130RPCh. 8.8 - Nitrogen gas enters a diffuser at 100 kPa and 110C...Ch. 8.8 - Obtain a relation for the second-law efficiency of...Ch. 8.8 - Writing the first- and second-law relations and...Ch. 8.8 - Prob. 134RPCh. 8.8 - Prob. 136FEPCh. 8.8 - Prob. 137FEPCh. 8.8 - A heat engine receives heat from a source at 1500...Ch. 8.8 - Prob. 139FEPCh. 8.8 - Prob. 140FEPCh. 8.8 - A 12-kg solid whose specific heat is 2.8 kJ/kgC is...Ch. 8.8 - Keeping the limitations imposed by the second law...Ch. 8.8 - A furnace can supply heat steadily at 1300 K at a...Ch. 8.8 - Air is throttled from 50C and 800 kPa to a...Ch. 8.8 - Prob. 145FEP
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