To determine The temperature after throttling. The comparison with value obtained using ideal gas model. Explanation Write the expression for throttling process. h ¯ * 2 ( T 2 ) − R ¯ T c ( h ¯ * − h ¯ R ¯ T c ) 2 = h ¯ * 1 ( T 1 ) − R ¯ T c ( h ¯ * − h ¯ R ¯ T c ) 1 (I) Here, molecular weight is M , critical temperature is T c , the universal gas constant is R ¯ , the temperature at state 1 is T 1 , the temperature at state 2 is T 2 , the molar specific enthalpy at state 1 is h ¯ * 1 ( T 1 ) , the molar specific enthalpy at state 2 is h ¯ * 2 ( T 2 ) , the enthalpy departure at state 1 is ( h ¯ * − h ¯ R ¯ T c ) 1 and the enthalpy departure at state 2 is ( h ¯ * − h ¯ R ¯ T c ) 2 . The expression across the valve adheres to the throttling process model, for which h 1 = h 2 . Write the expression for reduced temperature at state 1 . T R 1 = T 1 T c (II) 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 (III) 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 (IV) 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 (V) Here, the reduced pressure state 2 is p R 2 . Write the expression for error percentage. E = ( T s − T 1 T s ) × 100 (VI). Here, the temperature from the steam table is T s and the error percentage is E Conclusion: Substitute 154 K for T c and 300 K for T 1 in Equation (II). T R 1 = 300 K 154 K = 1.94 Substitute 154 K for T c and 280 K for T 2 in Equation (III). T R 2 = 280 K 154 K = 1.82 Substitute 50.5 bar for p c and 100 bar for p 1 in Equation (IV). p R 1 = 100 bar 50.5 bar = 1.98 Substitute 50.5 bar for p c and 20 bar for p 2 in Equation (V). p R 2 = 20 bar 50.5 bar = 0.40 Refer to the Table A-1 “Ideal Atomic or Molecular Weights and Critical Properties of Selected Elements and Compounds” to obtain the critical temperature is 154 K , the critical pressure is 50.5 bar and molecular weight is 32 kg / mole ⋅ K of oxygen gas

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832318

Author: MORAN

Publisher: WILEY

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Chapter 11.9, Problem 89P

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The temperature after throttling.

The comparison with value obtained using ideal gas model.

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Chapter 11.9, Problem 88P

Chapter 11.9, Problem 90P

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Fundamentals of Engineering Thermodynamics

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