a) Explanation Draw the given Otto cycle on P − v diagram as in Figure (1). Write the relation between the temperature and specific volume for the isentropic compression process 1-2 from Figure (1). 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 pressure, temperature, and specific volume relation for isentropic compression process 1-2 as P 2 v 2 T 2 = P 1 v 1 T 1 P 2 = v 1 v 2 P 1 T 1 T 2 (II) Here, pressure at state 1 is P 1 , and pressure at state 2 is P 2 . For constant volume heat addition process 2-3, express the heat addition ( q 23 , in ) as q 23 , i n = c v ( T 3 − T 2 ) (III) Here, specific heat at constant volume is c v , temperature at state 3 is T 3 . Write the relation between the temperature, pressure, and specific volume relation for the constant volume heat addition process 2-3. P 3 v 3 T 3 = P 2 v 2 T 2 P 3 = P 2 v 2 T 2 T 3 (IV) For process 2-3, v 2 and v 3 are equal. Here, pressure at state 3 is P 3 , and specific volume at state 3 is v 3 . From the Table A-2 “Ideal2gas specific heats of various common gases” obtain the below properties for air. c v = 0.718 kJ / kg ⋅ K c p = 1.005 kJ / kg ⋅ K R = 0.287 kJ / kg ⋅ K k = 1.4 Conclusion. Substitute 300 K for T 1 , 8 for ( v 1 v 2 ) , and 1 b) To determine The net work output for the given Otto cycle c) To determine The thermal efficiency of the given Otto cycle. d) To determine The mean effective pressure of the given Otto cycle.

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Chapter 9.12, Problem 35P

To determine

The temperature and pressure at the end of the heat addition process

To determine

The net work output for the given Otto cycle

To determine

The thermal efficiency of the given Otto cycle.

To determine

The mean effective pressure of the given Otto cycle.

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Chapter 9.12, Problem 33P

Chapter 9.12, Problem 36P

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The temperature and pressure at the end of the heat addition process

Solution Summary: The author explains the temperature and pressure at the end of the heat addition process for the given ideal Otto cycle.

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The temperature and pressure at the end of the heat addition process

The net work output for the given Otto cycle

The thermal efficiency of the given Otto cycle.

The mean effective pressure of the given Otto cycle.

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Chapter 9 Solutions