Concept explainers
a)
The thermal efficiency of an ideal diesel cycle using constant specific heats.
a)
Answer to Problem 161RP
The thermal efficiency of ideal diesel cycle is
Explanation of Solution
Draw
Assuming constant specific heats
Write the temperature and specific volume relation for the isentropic compression process 1-2.
Here, the specific heat ratio is
Write the ideal gas relation for the constant pressure heat addition process 2-3.
For the process 2-3,
Here, temperature at state 3 is
Write the expression of heat input to the cycle
Here, the specific heat at constant pressure is
Write the temperature and specific volume relation for isentropic expansion process 3-4.
Write the expression of heat rejected for constant volume heat rejection process 4-1
Here, specific heat at constant volume is
Write the expression to calculate the net work output of the engine
Write the expression of thermal efficiency of the ideal diesel cycle
Conclusion:
From Table A-2a, “Ideal-gas specific heats of various common gases”, obtain the following properties of air at room temperature.
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the thermal efficiency of an ideal diesel cycle is
b)
The thermal efficiency of ideal diesel cycle using variable specific heats.
b)
Answer to Problem 161RP
The thermal efficiency of an ideal diesel cycle is
Explanation of Solution
Assuming variable specific heats
Write the specific volume and relative specific volume relation for the isentropic compression process 1-2.
Here, the compression ratio is r, relative specific volume at state 1 is
Write the pressure, temperature, and specific volume relation for isentropic compression process 2-3.
For process 2-3,
Write the expression of heat addition for constant pressure heat addition process 2-3
Write the specific volume and relative specific volume relation for the isentropic expansion process 3-4.
Here, relative specific volume at state 4 is
Write the expression of heat rejected for constant volume heat rejection process 4-1
Write the expression of thermal efficiency of an deal diesel cycle
Conclusion:
Refer Table A-17, “Ideal gas properties of air”, obtain the following properties of air at temperature
Substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at
Substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at
Substitute
Substitute
Refer Table A-17, “Ideal gas properties of air”, obtain the properties of air at
Substitute
Substitute
Thus, the thermal efficiency of an ideal diesel cycle is
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Chapter 9 Solutions
Thermodynamics: An Engineering Approach
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