Explanation Draw P − v diagram for diesel cycle as shown in Figure (1). Write the relation between the specific volume, and relative specific volume for the isentropic compression process 1-2. v r 2 = v 2 v 1 v r 1 v r 2 = 1 r v r 1 (I) Here, the compression ratio is r , relative specific volume at state 1 is v r 1 , relative specific volume at state 2 is v r 2 , specific volume at state 1 is v 1 and specific volume at state 2 is v 2 . Write the ideal gas relation for the constant pressure heat addition process 2-3. P 3 v 3 T 3 = P 2 v 2 T 2 For the process 2-3, P 2 = P 3 v 3 T 3 = v 2 T 2 v 3 v 2 = T 3 T 2 (II) Here, pressure at state 3 is P 3 , pressure at state 2 is P 2 , specific volume at state 3 is v 3 , temperature at state 3 is T 3 and temperature at state 2 is T 2 . Write the expression of heat input to the cycle ( q i n ) . q i n = h 3 − h 2 (III) Here, enthalpy at state 3 is h 3 and enthalpy at state 2 is h 2 . Write the relation between the specific volume, and relative specific volume for the isentropic expansion process 3-4. v r 4 = v 4 v 3 v r 3 (IV) Here, relative specific volume at state 4 is v r 4 , relative specific volume at state 3 is v r 3 , specific volume at state 4 is v 4 and specific volume at state 3 is v 3 . Write the expression of heat rejected for constant volume heat rejection process 4-1 ( q out ) . q out = u 4 − u 1 (V) Here, internal energy at state 4 is u 4 and internal energy at state 1 is u 1 . Write the pressure and temperature relation for the process 4-1. P 4 P 1 = T 4 T 1 P 4 = P 1 T 4 T 1 (VI) Here, pressure at state 4 is P 4 , pressure at state 1 is P 1 and temperature at state 4 is T 4 . Write the expression of entropy change for the process 4-1 ( s 1 − s 4 ) . s 1 − s 4 = s 1 @ 580 R ∘ − s 4 @ 1531.8 R ∘ − R ln P 1 P 4 (VII) Write the expression of exergy destruction associated with the heat rejection process of the Diesel cycle ( x destroyed,41 ) . x destroyed,41 = T 0 ( s 1 − s 4 + q out T R ) (VIII) Here, the temperature of the surroundings is T 0 , and the temperature of the sink is T R . Write the expression of exergy at the end of the expansion stroke ( ϕ 4 ) . ϕ 4 = ( u 4 − u 0 ) − T 0 ( s 4 − s 0 ) + P 0 ( v 4 − v 0 ) (IX) Here, the specific entropy at state 4 is s 4 , the specific entropy of the surroundings is s 0 , pressure of the surroundings is P 0 , specific volume of the surroundings is v 0 , and specific internal energy of the surroundings is u 0 . Conclusion: Refer Table A-17E, “Ideal gas properties of air”, obtain the properties of air at 580 R ( T 1 ) , as 98.90 Btu / lbm for u 1 , and 120.70 for v r 1 . Substitute 18.2 for r and 120.70 for v r 1 in Equation (I). v r 2 = 1 18.2 120.70 = 6.632 Refer Table A-17E, “Ideal gas properties of air”, obtain the properties of air at 6.632 ( v r 2 ) as 1,725.8 R for T 2 , and 429.56 Btu / lbm for h 2 . Substitute 3,200 R for T 3 , and 1,725.8 R for T 2 in Equation (II). v 3 v 2 = 3 , 200 R 1 , 725.8 R = 1.854 Refer Table A-17E, “Ideal gas properties of air”, obtain the properties of air at 3200 R ( T 3 ) , as 849.48 Btu / lbm for h 3 , and 0

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Author: CENGEL

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Chapter 9.12, Problem 144P

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The exergy destruction associated with the heat rejection process of the given Diesel cycle and the exergy at the end of the isentropic expansion process.

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Chapter 9.12, Problem 143P

Chapter 9.12, Problem 145P

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A Diesel cycle has air as the working fluid. The air begins the compression process at 100kPa and 40C. During the heat addition process, 1200 kJ/kg of heat is added to the air. The compression ratio of the cycle is 18. Treating the air as an ideal gas with constant specific heats, determine (a) the temperature and pressure at each state point, (b)the network per unit mass, (c) the thermal efficiency of the cycle and (d) Mean effective pressure.

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In a cold-air standard diesel cycle, the volume of the cylinder amounts to 85 cm3 at the beginning of the heat addition process, 175 cm3 at the end, and 1300 cm3 at the beginning of the heat rejection process. If air is at 19.5°C and 118 kPa at the end of the heat rejection process, determine the (a) thermal efficiency, in % (b) mean effective pressure, in kPa (c) the pressure at the end of the isentropic expansion process, in kPa. Illustrate the T-s and P-? diagrams. Use ??= 0.718 kJ/kg-K, ??= 1.005 kJ/kg-K and ?= 1.4, where applicable. Use g = 9.81 m/s2 or 32.2 ft/s2 , T(K)=T(°C)+273 and T(R)=T(°F)+460, where applicable

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EBK THERMODYNAMICS: AN ENGINEERING APPR

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The exergy destruction associated with the heat rejection process of the given Diesel cycle and the exergy at the end of the isentropic expansion process.

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The exergy destruction associated with the heat rejection process of the given Diesel cycle and the exergy at the end of the isentropic expansion process.

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