To determine The heat transfer in kJ / kg of carbon dioxide. The work transfer in kJ / kg of carbon dioxide. Explanation The figure below shows the flow of carbon dioxide gas through a turbine. Figure-(1) The gas constant flows through ( 1 ) to ( 2 ) . The rate of heat transfer through the control volume is Q ˙ c v , the mass flow rate is m ˙ and the rate of work transfer through the control volume is W ˙ c v . The temperature a inlet and exit is same that is T . Write the expression for the heat transfer per unit mass flow rate through the control volume. Q ˙ c v m ˙ = T ( s 2 − s 1 ) (I) Here, the temperature is T , the specific entropy at state 1 is s 1 and the specific entropy at state 2 is s 2 . Write the expression for specific entropy change for an ideal gas. s 2 − s 1 = [ s ( T 2 ) − s ° ( T 1 ) − R ln ( p 2 p 1 ) ] (II) Here, the entropy variable depended on temperature ( T 1 ) is s ° ( T 1 ) , the entropy variable depended on temperature ( T 2 ) is s ° ( T 2 ) , the gas constant is R , the pressure at state 1 is p 1 and the pressure at state 2 is p 2 . The inlet and exit temperature is same hence s ° ( T 1 ) and s ° ( T 2 ) are equal. Substitute s ° ( T 2 ) for s ° ( T 1 ) in Equation (II). s 2 − s 1 = [ s ( T 2 ) − s ° ( T 2 ) − R ln ( p 2 p 1 ) ] = [ − R ln ( p 2 p 1 ) ] (III) Substitute [ − R ln ( p 2 p 1 ) ] for s 2 − s 1 in Equation (I). Q ˙ c v m ˙ = T [ − R ln ( p 2 p 1 ) ] (IV) Write the steady flow energy equation for the turbine. W ˙ c v + m ˙ { v 2 2 2 + g z 2 } = Q ˙ c v + m ˙ { v 1 2 2 + g z 1 } W ˙ c v = Q ˙ c v + m ˙ { v 1 2 2 + g z 1 } − m ˙ { v 2 2 2 + g z 2 } W ˙ c v = Q ˙ c v + m ˙ { v 1 2 2 − v 2 2 2 } + m ˙ { g z 1 − g z 2 } (V) Here, the datum head at 1 is z 1 , the datum head at 2 is z 2 , the acceleration due to gravity is g , the velocity at 1 is v 1 and the velocity at 2 is v 2 . The potential and kinetic energy changes are assumed to be negligible hence, final velocity will be equal to the initial velocity and the initial datum head will be equal to the final datum head. Substitute v 1 for v 2 and z 2 for z 1 in Equation (V)

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 6.13, Problem 171P

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The work transfer in kJ/kg of carbon dioxide.

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Chapter 6.13, Problem 170P

Chapter 6.13, Problem 172P

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Fundamentals of Engineering Thermodynamics

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The heat transfer in kJ/kg of carbon dioxide.

The work transfer in kJ/kg of carbon dioxide.