a) Explanation Draw P − v diagram for an Ideal diesel cycle as shown in Figure (1). Write temperature and specific volume relation for the isentropic compression process 1-2. T 2 = T 1 ( v 1 v 2 ) k − 1 (I) 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 , and the specific heat ratio is k . Write the temperature, pressure, and specific volume relation for the constant pressure heat addition process 2-3. P 3 v 3 T 3 = P 2 v 2 T 2 P 2 and P 3 are equal for process 2-3. v 3 v 2 = T 3 T 2 (II) Here, the temperature at state 3is T 3 , specific volume at state 2 is v 2 , specific volume at state 3 is v 3 , pressure at state 3 is P 3 , pressure at state 2 is P 2 , and specific volume at state 3 is v 3 . Write the expression for constant pressure heat addition process 2-3 ( q in ) . q i n = c p ( T 3 − T 2 ) (III) Here, the specific heat at constant pressure is c p . Write the temperature and specific volume relation for isentropic expansion process 3-4. T 4 = T 3 ( v 3 v 4 ) k − 1 (IV) Here, temperature at state 4 is T 4 , and specific volume at state 4 is v 4 . Write the expression for constant volume heat rejection process 4-1 ( q o u t ) . q o u t = u 4 − u 1 = c v ( T 4 − T 1 ) (V) Here, specific heat at constant volume is c v , internal energy at state 1 is u 1 , and internal energy at state 4 is u 4 . Write the expression to calculate the net work output for the cycle ( w net,out ) . w net,out = q in − q out (VI) Write the expression to calculate the thermal efficiency of the cycle ( η t h ) . η t h = w net,out q in (VII) Conclusion: From Table A-2a, “Ideal-gas specific heats of various common gases”, obtain the following properties of air at room temperature. c p = 1.005 kJ / kg ⋅ K c v = 0.718 kJ / kg ⋅ K R = 0.287 kJ / kg ⋅ K k = 1.4 Substitute 20 ° C for T 1 , 20 for ( v 1 v 2 ) , and 1.4 for k in Equation (I). T 2 = ( 20 ° C ) ( 20 ) 1.4 − 1 = ( 20 + 273 ) K × ( 20 ) 1.4 − 1 = 971.1 K P 2 and P 3 are equal for process 2-3 b) To determine The mean effective pressure an ideal diesel cycle.

9th Edition

ISBN: 9781259822674

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

Publisher: McGraw-Hill Education

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Chapter 9.12, Problem 57P

To determine

The thermal efficiency of an ideal diesel cycle.

To determine

The mean effective pressure an ideal diesel cycle.

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Chapter 9.12, Problem 56P

Chapter 9.12, Problem 58P

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Thermodynamics: An Engineering Approach

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