Explanation Draw the P − ν diagram for an ideal Otto cycle as shown in Figure (1). Consider, the pressure is P i , the specific volume is v i , the temperature is T i , the entropy is s i , the enthalpy is h i corresponding to i t h state. F o r c o m p r e s s i o n r a t i o ( r ) . Write the expression for temperature at the end of the compression process 1-2. T 2 T 1 = ( v 1 v 2 ) k − 1 T 2 = T 1 ( r ) k − 1 Here , specific heat ratio is k and compression ratio is r . The temperature rise during combustion remains constant. Thus, the amount of heat addition remains constant Write the expression for maximum temperature. q i n = c v ( T 3 − T 2 ) kJ / kg T 3 = q i n c v + T 2 (I) Here, specific heat at constant volume is c v Write the expression to obtain smallest gas specific volume at state 3 ( v 3 ) during the cycle. v 3 = v 1 r Ideal gas equation is applied for sate 3. P 3 v 3 = R T 3 P 3 = R T 3 v 3 (II) T h e c o m p r e s s i o n r a t i o i s d o u b l e d ( 2 r ) : Write the expression for temperature at the end of the compression process 1-2 when the compression ratio is doubled. T 2 ' T 1 ' = ( 2 r ) k − 1 T 2 ' = T 1 ' ( 2 r ) k − 1 Write the expression for maximum temperature ( T 3 ) when the compression ratio is doubled. q i n = c v ( T 3 ' − T 2 ' ) kJ / kg T 3 ' = q i n c v + T 2 ' (III) Write the expression to obtain smallest gas specific volume at state 3 ( v 3 ) when the compression ratio is doubled. v 3 ' = v 1 ' 2 r Ideal gas equation is applied for sate 3 when the compression ratio is doubled. P 3 ' v 3 ' = R T 3 ' P 3 ' = R T 3 ' v 3 ' (IV) Conclusion: Substitute T 1 ( r ) k − 1 for T 2 in Equation (I)

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ISBN: 8220100257056

Author: CENGEL

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Chapter 9.12, Problem 40P

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What happens to the maximum gas temperature, pressure and heat addition when the compression ratio is doubled for an ideal Otto cycle?

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Chapter 9.12, Problem 39P

Chapter 9.12, Problem 41P

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What happens to the maximum gas temperature, pressure and heat addition when the compression ratio is doubled for an ideal Otto cycle?

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