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.

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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Chapter 9.12, Problem 54P

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 53P

Chapter 9.12, Problem 55P

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An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, determine the mean effective pressure. Assume constant specific heats for air at room temperature.

An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, draw the cycle on p-v and t-s diagrams and calculate the thermal efficiency.

An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20 °C. If the maximum temperature in the cycle is not to exceed 2200 K, determine a) the thermal efficiency and b) the mean effective pressure. Take cv = 718 j/kg/K, cp = 1005 j/kg/K and R = 287 j/kg/K

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