Explanation Draw the P − v diagram for an ideal diesel 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. Write the expression for ideal temperature ( T 2 s ) at the end of the compression process. T 2 s = T 1 ( v 2 v 1 ) ( k − 1 ) = T 1 ( r ) ( k − 1 ) (I). Here, the specific heat ratio is k and compression ratio is r . Write the expression for efficiency isentropic compression ( η C ) to calculate actual temperature at the end of the compression. η C = ( T 2 s − T 1 ) ( T 2 − T 1 ) T 2 = T 1 + ( T 2 s − T 1 ) η C (II). Write the expression to calculate the maximum temperature. T 3 = T 2 ( v 3 v 2 ) = T 2 ( r c ) (III). Write the temperature and pressure relation ratio for the expansion process 3-4 s . T 4 s = T 3 ( v 3 v 4 ) ( k − 1 ) = T 3 ( r c v 2 r v 2 ) ( k − 1 ) = T 3 ( r c r ) ( k − 1 ) (IV). Write the expression for the isentropic efficiency of the turbine ( η T ) to calculate actual temperature at the end of the expansion process. η T = ( T 3 − T 4 ) ( T 3 − T 4 s ) T 4 = T 3 − η T ( T 3 − T 4 s ) (V). The net work production is calculated by the difference between the work produced by the expansion process, and that produced work is gained by the compression. Write the expression to calculate the net work production. w net = c v ( T 3 − T 2 ) − c v ( T 2 − T 1 ) = c v [ ( T 3 − T 2 ) − ( T 2 − T 1 ) ] (VI). Here, specific heat at constant pressure is c v . Write the expression to calculate the heat input ( q i n ) during heat addition process 2-3. q i n = c p ( T 3 − T 2 ) (VII). Here, specific heat at constant pressure is c p . Write the expression to calculate the thermal efficiency of the cycle. η t h = w n e t q i n (VIII). Write the expression to calculate the rate of heat addition ( Q ˙ i n ) to the cycle when it produces 200 hp of power ( W ˙ n e t ) . Q ˙ i n = W ˙ n e t η t h (IX). Conclusion: Refer Table A-2a, “Ideal-gas specific heats of various common gases”, obtain the following properties of air at room temperature. R = 0.287 kPa ⋅ m 2 / kg ⋅ K c p = 1.005 kJ / kg ⋅ K c v = 0.718 kJ / kg ⋅ K k = 1

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Chapter 9.12, Problem 51P

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The maximum air temperature and the rate of heat addition to the cycle when it produces 200 hp of power.

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Chapter 9.12, Problem 50P

Chapter 9.12, Problem 52P

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An ideal Diesel cycle has a compression ratio of 18 and a cutoff ratio of 1.5. Determine the maximum air temperature and the rate of heat addition to this cycle when it produces 200 hp of power; the cycle is repeated 1200 times per minute; and the state of the air at the beginning of the compression is 95 kPa and 17°C. Use constant specific heats at room temperature.

An air-standard Diesel cycle has a compression ratio of 18 and a cutoff ratio of 1.8. At the beginning of the compression process, air is at 95 kPa and 27°C. Using constant specific heats at room temperature, determine the thermal efficiency for the cycle. Use cp= 1.005 kJ/kgK and cv-0.718 kJ/kgK. Please keep one decimal for the final answer.

An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2.5. At the beginning of the compression process, air is at 95 kPa and 27°C. Accounting for the variation of specific heats with temperature, plot the cycle on P-v and T-s diagrams and then determine:- (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure.

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The maximum air temperature and the rate of heat addition to the cycle when it produces 200 hp of power.

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