(a) To determine The fan power. Explanation Write energy rate balance Equation for 1-2. − W = − ( m 2 − m 1 ) h i n + m 2 u 2 − m 1 u 1 (I) Here, work is W , final mass is m 2 , initial mass is m 1 , final specific internal energy is u 2 and te initial internal energy is u 1 . Substitute 0 for m 1 in equation (I). − W = − ( m 2 − 0 ) h i n + m 2 u 2 − ( 0 ) u 1 − W = − m 2 h i n + m 2 u 2 (II) Write the expression for work during expansion. W exp = p ( V 2 − V 1 ) (III) Here, work during expansion is W exp , final volume is V 2 and the initial volume is V 1 . Write the expression for gas constant. R = R ¯ M (IV) Here, gas constant is R , universal gas constant is R ¯ and the molecular mass is M . Write the expression for final mass. m 2 = p 2 V 2 R T 2 (V) Here, final state pressure is p 2 and the final temperature is T 2 . Write the expression for fan power. W ˙ f a n = W − W exp t (VI) Here, fan power is W ˙ f a n and the time is t . Conclusion: Substitute 14.7 lb / in 2 for p , 49000 ft 3 for V 2 and 0 for V 1 in Equation (III). W exp = ( 14.7 lb / in 2 ) ( 49000 ft 3 − 0 ) = ( 14.7 lb / in 2 ) ( 1 ft 12 in ) 2 ( 49000 ft 3 ) = ( 14.7 lb / in 2 ) ( 1 ft 12 in ) 2 ( 49000 ft 3 ) ( 1 Btu 778 lb ⋅ ft ) = 133592.39 Btu Substitute 1545 ft ⋅ lb / lbmol ⋅ °R for R ¯ and 28.97 lb / lbmol for M in Equation (IV) (b) To determine The time required.

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 4.12, Problem 130P

(a)

To determine

The fan power.

(b)

To determine

The time required.

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Chapter 4.12, Problem 128P

Chapter 5.11, Problem 1E

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