Explanation Write the expression for the masses and energy state. ( W ˙ c v m ˙ ) = ( Q ˙ c v m ˙ ) + ( h 1 − h 2 ) (I) Here, work flow rate is W ˙ c v , the mass flow rate is m ˙ , the heat flow rate is Q ˙ c v , the specific enthalpy at state 1 is h 1 and the specific enthalpy at state 2 is h 2 . The expansion process in turbine is adiabatic process hence Q ˙ c = 0 . Substitute 0 for Q ˙ c in Equation (I). ( W ˙ c v m ˙ ) = 0 + ( h 1 − h 2 ) = ( h 1 − h 2 ) (II) Write the expression for change in enthalpy. W ˙ c v m ˙ = h ¯ 1 * ( T 1 ) − h ¯ * 2 ( T 2 ) − R ¯ T c [ ( h ¯ * − h R ¯ T c ) 1 − ( h ¯ * − h R ¯ T c ) 2 ] M (III) Here, the molecular weight is M , the universal gas constant is R ¯ , the molar enthalpy at state 1 at temperature T 1 is h ¯ 1 * ( T 1 ) , the molar specific enthalpy at state 2 at temperature T 2 is h ¯ * 2 ( T 2 ) , the temperature at critical point is T c , the temperature at point 1 is T 1 and the temperature at point 2 is T 2 . Write the expression for the change in the specific entropy. s 2 − s 1 = s ¯ ° ( T 2 ) − s ¯ ° ( T 1 ) − R ¯ l ¯ n ( p 2 p 1 ) (IV) Here, the specific entropy at state 1 is s 1 , the specific entropy at state 2 is s 2 , the molar specific entropy at temperature T 1 is s ¯ ° ( T 1 ) , the molar specific entropy at temperature T 2 is s ¯ ° ( T 1 ) the pressure at state 1 is p 2 and the pressure at state 2 is p 1 . Write the expression for entropy production. ( σ ˙ c v m ˙ ) = 1 M [ s 2 − s 1 − R ¯ [ [ s ¯ ∘ − s ¯ R ] 2 − [ s ¯ ∘ − s ¯ R ] 1 ] ] (V) Here, the gas constant is R , the enthalpy departure at state 1 is [ s ¯ ∘ − s ¯ R ] 1 , the enthalpy departure is [ s ¯ ∘ − s ¯ R ] 2 and the specific entropy production is ( σ ˙ c v m ˙ ) . Write the expression for reduced temperature at state 1 . T R 1 = T 1 T c (VI) Here, the reduced temperature at state 1 is T R 1 . Write the expression for reduced temperature at state 2 . T R 2 = T 2 T c (VII) Here, the reduced temperature at state 2 is T R 2 . Write the expression reduced pressure at state 1 . p R 1 = p 1 p c (VIII) Here, the reduced pressure state 1 is p R 1 . Write the expression reduced pressure at state 2 . p R 2 = p 2 p c (IX) Here, the reduced pressure state 2 is p R 2 . Write the expression for molar heat transfer rate. ( Q c v m ˙ ) = ( W ˙ c v m ˙ ) ( m ˙ ) (X) Here, the mass flow rate is m ˙ . Write the expression for entropy production. σ c v = ( σ ˙ c v m ˙ ) ( m ˙ ) (XI) Conclusion: Substitute 154 K for T c and 287 K for T 1 in Equation (VI). T R 1 = 287 K 154 K = 1

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 11.9, Problem 87P

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Power required for compressor in kW.

The rate of the entropy production.

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Chapter 11.9, Problem 86P

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Power required for compressor in kW . The rate of the entropy production.

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Power required for compressor in kW.

The rate of the entropy production.