Concept explainers
(a)
The temperature at the end of expansion process.
(a)
Answer to Problem 167RP
The temperature at the end of expansion process is
Explanation of Solution
Determine the state 2 temperature in the polytropic compression process 1-2.
Here, the state 1 temperature is
Determine the state 2 pressure in the polytropic compression process 1-2.
Here, the state 1 pressure is
Determine the work per unit mass in the polytropic compression process 1-2.
Here, the universal gas constant is
Determine the state 3 temperature in the constant volume heat addition process 2-3.
Here, the state 2 temperature is
Determine the heat transfer per unit mass in the constant volume heat addition process 2-3.
Here, the specific heat of constant volume is
Determine the state 4 temperature in the polytropic expansion process 3-4.
Here, the specific volume at state 3 is
Determine the state 4 pressure in the polytropic expansion process 3-4.
Here, the state 3 pressure is
Determine the work per unit mass in the polytropic compression process 3-4.
Here, the universal gas constant is
Conclusion:
From the Table A-2 (a), “Ideal-gas specific heats of various common gases”, obtain the value of universal gas constant of air is
Refer to Table A-2 (b), “Ideal-gas specific heats of various common gases”, obtain the below properties at the average temperature of 850 K using interpolation method of two variables.
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y are temperature and specific heat of constant pressure.
Show the temperature at 800 K and 900 K as in Table (1).
S. No |
Temperature, K |
specific heat of constant pressure, |
1 | 800 K | 1.099 |
2 | 850 K | |
3 | 900 K | 1.121 |
Calculate specific heat of constant pressure at an average temperature of 850 K for liquid phase using interpolation method.
Substitute 800 K for
From above calculation the specific heat of constant pressure is
Similarly repeat the interpolation method for specific heat of constant volume and ratio of specific heat as:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the temperature at the end of expansion process is
Substitute
Substitute
(b)
The net-work output at the constant volume heat rejection.
The thermal efficiency at the constant volume heat rejection.
(b)
Answer to Problem 167RP
The net-work output at the constant volume heat rejection is
The thermal efficiency at the constant volume heat rejection is
Explanation of Solution
Determine the net-work output at the constant volume heat rejection.
Determine the thermal efficiency at the constant volume heat rejection.
Conclusion:
Substitute
Thus, the net-work output at the constant volume heat rejection is
Substitute
Thus, the thermal efficiency at the constant volume heat rejection is
(c)
The mean effective pressure at the constant volume heat rejection.
(c)
Answer to Problem 167RP
The mean effective pressure at the constant volume heat rejection is
Explanation of Solution
Determine the initial volume at the constant volume heat rejection.
Determine the mean effective pressure at the constant volume heat rejection.
Here, the compression ratio is
Note:
Conclusion:
Substitute
Substitute
Thus, the mean effective pressure at the constant volume heat rejection is
(d)
The engine speed for a given net power.
(d)
Answer to Problem 167RP
The engine speed for a given net power is
Explanation of Solution
Determine the clearance volume at the beginning of compression process.
Here, the volume of the gasoline engine is
Determine the initial volume.
Determine the total mass contained in the cylinder.
Determine the engine speed for a net power output of 50 kW.
Note: the two revolutions in one cycle in four-stroke engines.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the engine speed for a given net power is
(e)
The specific fuel consumption.
(e)
Answer to Problem 167RP
The specific fuel consumption is
Explanation of Solution
Determine the mass of fuel burned during one cycle.
Here, the air-fuel ratio is
Determine the specific fuel consumption.
Conclusion:
Substitute 16 for AF and
Substitute
Thus, the specific fuel consumption is
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