Explanation Write the expression for the work transfer at constant pressure. W n = R ¯ [ T 2 Z 2 − T 1 Z 1 ] (I) Here, the characteristic gas constant is R ¯ , the number of the moles is n , the temperature of the gas at final state is T 2 , temperature of the gas at initial state is T 1 , the compressibility factor at initial state is Z 1 and the compressibility factor final state is Z 2 . Write the expression for the reduced temperature at initial state. T R 1 = T 1 T C (II) Here, the critical temperature of the gas is T C and temperature of the gas at initial state is T 1 . Write the expression for the reduced temperature at final state. T R 2 = T 2 T C (III) Here, temperature of the gas at final state is T 2 . Write the expression for the reduced pressure. p r = p p C (IV) Here, the pressure of the gas is p and the critical pressure is p C . Write the expression for the transfer of heat for the process. h ¯ 2 − h ¯ 1 = h ¯ * 2 − h ¯ 1 − R ¯ T C [ ( h ¯ * − h ¯ R ¯ T C ) 2 − ( h ¯ * − h ¯ R ¯ T C ) 1 ] Q n = h ¯ * 2 − h ¯ 1 − R ¯ T C [ ( h ¯ * − h ¯ R ¯ T C ) 2 − ( h ¯ * − h ¯ R ¯ T C ) 1 ] (V) Here, the enthalpy departure value corresponds to initial temperature is h ¯ * 1 , the enthalpy departure value corresponds to final temperature is h ¯ 2 , enthalpy departure at reduced pressure and temperature at initial state is ( h ¯ * − h ¯ R ¯ T C ) 1 and enthalpy departure at reduced pressure and temperature at final state is ( h ¯ * − h ¯ R ¯ T C ) 2 . Conclusion: Refer to table A-1 “Atomic molecular weight and critical properties of selected elements and compounds” to obtain the critical properties of the nitrogen as molecular weight M = 28.01 kg / k ⋅ mol , critical temperature T C = 126 K and critical pressure p C = 33.9 bar . Substitute 220 K for T 1 and 126 K for T C in Equation (II). T R 1 = 220 K 126 K = 1.746 ≈ 1.75 Substitute 300 K for T 2 and 126 K for T C in Equation (III)

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 92P

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The heat transfer for the process.

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The work transfer for the process. The heat transfer for the process.