Explanation Draw the given ideal dual cycle on P − v diagram as in Figure (1) Write the expression to obtain the pressure at the end of compression ( P 2 ) . P 2 = P 1 ( v 1 v 2 ) k P 2 = P 1 r k (I) Write the expression of pressure using the pressure ratio for the process 2-3. P x = P 3 = ( r p ) ( P 2 ) (II) Here, the pressure ratio is r p and the maximum pressure is P x and P 3 . Write the expression of temperature and specific volume relation for the isentropic compression process 1-2. T 2 = T 1 ( v 1 v 2 ) k − 1 T 2 = T 1 ( r ) k − 1 (III) Here, the temperature at state 1 is T 1 , the temperature at state 2 is T 2 , specific volume at state 1 is v 1 , specific volume at state 2 is v 2 , the specific heat ratio is k and the compression ratio is r . Write the expression of temperature and pressure for the process 2-3. T x = T 2 ( P 3 P 2 ) (IV) Here, temperature at state x is T x . Write the expression of temperature and specific volume relation to obtain the temperature at state 3 ( T 3 ) . T 3 = T x ( v 3 v x ) (V) Here, volume at state 3 is ν 3 and volume at state x is ν x . Write the expression of temperature and specific volume relation for the isentropic expansion process 3-4. T 4 = T 3 ( r c r ) k − 1 (VI) Here, temperature at state 4 is T 4 , specific volume at state 4 is v 4 , the compression ratio is r .and cutoff ratio is r c . Write the expression of heat addition ( q i n ) from the first law. q i n = c v ( T x − T 2 ) + c p ( T 3 − T x ) (VII) Here, specific heat at constant volume is c v and specific heat at constant pressure is c p . Write the expression of heat rejected ( q o u t ) for the constant volume heat rejection process 4-1. q o u t = c v ( T 4 − T 1 ) (VIII) Write the expression of thermal efficiency of the cycle ( η t h ) . η t h = 1 − q out q in (IX) Conclusion: From Table A-2Ea, “Ideal-gas specific heats of various common gases”, obtain the following properties for air. c v = 0 .171 Btu / lbm ⋅ R c p = 0.240 Btu / lbm ⋅ R k = 1.4 Substitute 14 psia for P 1 , 1.4 for k and 12 for r in Equation (I). P 2 = 14 psia × ( 12 ) 1.4 = 453.9 psia Substitute 1.2 for r p , and 453.9 psia for P 2 in Equation (II). P x = P 3 = ( 1

Thermodynamics: An Engineering Approach ( 9th International Edition ) ISBN:9781260092684

9th Edition

ISBN: 9781260048667

Author: Yunus A. Cengel Dr.; Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 9.12, Problem 66P

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Chapter 9.12, Problem 65P

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The maximum pressure, the maximum temperature, the amount of heat added and the thermal efficiency.

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