Explanation Show the given diesel cycle on P − ν diagram as in Figure (1). Write the expression of temperature and volume relation for the isentropic compression process 1-2. T 2 = T 1 ( ν 1 ν 2 ) k − 1 (I) Here, the specific heat ratio is k , temperature at state 1 and 2 is T 1 and T 2 , volume at state 1 and 2 is ν 1 and ν 2 , Write the expression of temperature, pressure, and volume relation for the constant pressure heat addition process 2-3. P 3 ν 3 T 3 = P 2 ν 2 T 2 (II) Here, pressure 1 and 2 is P 1 and P 2 , volume at state 3 is ν 3 and temperature at state 3 and 2 is T 3 and T 2 . Write the expression of temperature, and volume relation for the isentropic expansion process 3-4. T 4 = T 3 ( ν 3 ν 4 ) k − 1 (III) Here temperature at state 4 is T 4 and volume at state 4 is ν 4 . Write the expression of ideal gas equation for air at state 1 of the given diesel cycle. m = P 1 ν 1 R T 1 (IV) Here, mass of nitrogen is m , and gas constant is R . Write the expression of heat input to the cycle ( Q in ) . Q in = m ( h 3 − h 2 ) Q in = m c p ( T 3 − T 2 ) (V) Here, the specific heat at constant pressure is c p and enthalpy at stat 3 and 2 is h 3 and h 2 . Write the expression of heat rejected from the cycle ( Q out ) . Q out = m ( u 4 − u 1 ) Q out = m c v ( T 4 − T 1 ) (VI) Here, the specific heat at constant volume is c v and internal energy at state 4 and 1 is u 4 and u 1 . Write the expression of net work output per revolution by the cycle ( W net,out ) . W net,out = Q in − Q out (VII) Write the expression of power developed by the engine ( W ˙ net,out ) . W ˙ net,out = n ˙ W net,out (VIII) Here, the speed of the engine is n ˙ . Conclusion: Substitute 70 ° C for T 1 , 22 for ν 1 ν 2 , and 1.4 for k in Equation (I). T 2 = ( 70 ° C ) ( 22 ) 1.4 − 1 = ( 70 + 273 ) K ( 22 ) 0.4 = 1181 K For process 2-3, P 2 and P 3 are equal, as pressure remains constant. Substitute 1.8 for ν 3 ν 2 , and 1181 K for T 2 in Equation (II). T 3 = ( 1.8 ) ( 1181 K ) = 2126 K Substitute 1.4 for k , 1.8 ν 2 for ν 3 , ν 1 for ν 4 , 22 for r , and 2126 K for T 3 in Equation (III). T 4 = T 3 ( 1.8 ν 2 ν 1 ) 1.4 − 1 = T 3 ( 1.8 r ) 0.4 = ( 2126 K ) ( 1

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Chapter 9.12, Problem 61P

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The amount of power the engine will deliver at 2,300 rpm.

Solution Summary: The author shows the given diesel cycle on P-nu diagram as in Figure (1). Write the expression of temperature and volume relation for the isentropic compression process 1-2.

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The amount of power the engine will deliver at 2,300 rpm.

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