Explanation The p - v diagram for the Otto cycle is shown below. Figure-(1) The T - s diagram for the Otto cycle is shown below. Figure-(2) Write the expression for relation between, temperature and compression ratio for process 1-2. T 1 T 2 = r c γ − 1 (I) Here, the temperature at compressor outlet is T 2 , the compressor inlet is T 1 and the compression ratio is r c . Write the expression for relation between, temperature and compression ratio for process 3-4. T 3 T 4 = r c γ − 1 (II) Here, the temperature after expansion of the charge is T 4 , before expansion of the charge is T 3 and the compression ratio is r c . Write the expression for the net work of the cycle. W n e t = c v ( T 3 − T 2 + T 1 − T 4 ) (III) Here, the specific heat of the air at constant volume is c v . Conclusion: For r c = 5 and T 3 = 1000 K : Substitute 295 K for T 1 and 5 for r c and 1.4 for γ in Equation (I). T 2 295 K = 5 1.4 − 1 T 2 = ( 295 K ) × 1.90 T 2 = 561 K Substitute 1000 K for T 3 and 5 for r c and 1.4 for γ in Equation (II). 1000 K T 4 = 5 1.4 − 1 T 4 = 1000 K 1.9 T 4 = 526 K Substitute 0.718 kJ / kg ⋅ K for c v , 1000 K for T 3 , 526 K for T 4 , 561 K for T 2 , 295 K for T 1 in Equation.(III). W n e t = ( 0.718 kJ / kg ⋅ K ) × ( 1000 K − 561 K + 295 K − 526 K ) = ( 0.718 kJ / kg ⋅ K ) × 208 K = 149.34 kJ / kg For r c = 8 and T 3 = 1000 K : Substitute 295 K for T 1 and 8 for r c and 1.4 for γ in Equation (I). T 2 295 K = 8 1.4 − 1 T 2 = ( 295 K ) × 2.3 T 2 = 679 K Substitute 1000 K for T 3 and 8 for r c and 1.4 for γ in Equation (II). 1000 K T 4 = 8 1.4 − 1 T 4 = 1000 K 2.3 T 4 = 435 K Substitute 0.718 kJ / kg ⋅ K for c v , 1000 K for T 3 , 435 K for T 4 , 679 K for T 2 , 295 K for T 1 in Equation.(III). W n e t = ( 0.718 kJ / kg ⋅ K ) × ( 1000 K − 679 K + 295 K − 435 K ) = ( 0.718 kJ / kg ⋅ K ) × 181 K = 130 kJ / kg For r c = 11 and T 3 = 1000 K : Substitute 295 K for T 1 and 11 for r c and 1.4 for γ in Equation (I). T 2 295 K = 11 1.4 − 1 T 2 = ( 295 K ) × 2.61 T 2 = 770 K Substitute 1000 K for T 3 and 11 for r c and 1.4 for γ in Equation (II). 1000 K T 4 = 11 1.4 − 1 T 4 = 1000 K 2

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 9.14, Problem 16P

To determine

The effect of maximum cycle temperature of Otto cycles.

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Chapter 9.14, Problem 15P

Chapter 9.14, Problem 17P

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Fundamentals of Engineering Thermodynamics

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