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Imagine that a stream of fluid in steady-state flow serves as a heat source for an infinite set of Carnot engines, each of which absorbs a differential amount of heat from the fluid, causing its temperature to decrease by a differential amount, and each of which rejects a differential amount of heat to a heat reservoir at temperature T,. As a result of the operation of the Carnot engines, the temperature of the fluid decreases from T, to T2. Equation 5.8 applies here in differential form, wherein n is defined as: n = dW /dQ where Q is heat transfer with respect to the flowing fluid. Show that the total work of the Carnot engines is given by: w = Q- T, AS. where AS and Q both refer to the fluid. In the particular case the fluid is an ideal gas, Cp (7/2)R, for which T, = 600 K and T2 = 400 K. If T, = 300 K, what is the value of W in J mol1? How much heat is discarded to the heat reservoir at T,? What is the entropy change of the heat reservoir? What is AStotat?

Imagine that a stream of fluid in steady-state flow serves as a heat source for an infinite set of Carnot engines, each of which absorbs a differential amount of heat from the fluid, causing its temperature to decrease by a differential amount, and each of which rejects a differential amount of heat to a heat reservoir at temperature T,. As a result of the operation of the Carnot engines, the temperature of the fluid decreases from T, to T2. Equation 5.8 applies here in differential form, wherein n is defined as: n = dW /dQ where Q is heat transfer with respect to the flowing fluid. Show that the total work of the Carnot engines is given by: w = Q- T, AS. where AS and Q both refer to the fluid. In the particular case the fluid is an ideal gas, Cp (7/2)R, for which T, = 600 K and T2 = 400 K. If T, = 300 K, what is the value of W in J mol1? How much heat is discarded to the heat reservoir at T,? What is the entropy change of the heat reservoir? What is AStotat?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Imagine that a stream of fluid in steady-state flow serves as a heat source for an infinite set of Carnot engines, each of which absorbs a differential amount of heat from the fluid, causing its temperature to decrease by a differential amount, and each of which rejects a differential amount of heat to a heat reservoir at temperature T,. As a result of the operation of the Carnot engines, the temperature of the fluid decreases from T, to T2. Equation 5.8 applies here in differential form, wherein 7n is defined as: 1 = dW /dQ where Q is heat transfer with respect to the flowing fluid. Show that the total work of the Carnot engines is given by: W = Q - T, AS. where AS and Q both refer to the fluid. In the particular case the fluid is an ideal gas, Cp = (7/2)R, for which T, = 600 K and Tz = 400 K. If T, = 300 K, what is the value of W in J mol1? How much heat is discarded to the heat reservoir at T,? What is the entropy change of the heat reservoir? What is AStotal?
Transcribed Image Text:Imagine that a stream of fluid in steady-state flow serves as a heat source for an infinite set of Carnot engines, each of which absorbs a differential amount of heat from the fluid, causing its temperature to decrease by a differential amount, and each of which rejects a differential amount of heat to a heat reservoir at temperature T,. As a result of the operation of the Carnot engines, the temperature of the fluid decreases from T, to T2. Equation 5.8 applies here in differential form, wherein 7n is defined as: 1 = dW /dQ where Q is heat transfer with respect to the flowing fluid. Show that the total work of the Carnot engines is given by: W = Q - T, AS. where AS and Q both refer to the fluid. In the particular case the fluid is an ideal gas, Cp = (7/2)R, for which T, = 600 K and Tz = 400 K. If T, = 300 K, what is the value of W in J mol1? How much heat is discarded to the heat reservoir at T,? What is the entropy change of the heat reservoir? What is AStotal?
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