An air-standard dual cycle has a compression ratio of 9.1 and displacement of Vd = 2.2 L. At the beginning of compression, p1 = 95 kPa, and T1 = 290 K. The heat addition is 4.5 kJ, with one quarter added at constant volume and the rest added at constant pressure. Determine:a)    each of the unknown temperatures at the various states, in K.b)    the net work of the cycle, in kJ.c)    the power developed at 3000 cycles per minute, in kW.d)    the thermal efficiency.e)    the mean effective pressure, in kPa.

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Asked Jul 7, 2019
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An air-standard dual cycle has a compression ratio of 9.1 and displacement of Vd = 2.2 L. At the beginning of compression, p95 kPa, and T1 = 290 K. The heat addition is 4.5 kJ, with one quarter added at constant volume and the rest added at constant pressure. Determine:

a)    each of the unknown temperatures at the various states, in K.
b)    the net work of the cycle, in kJ.
c)    the power developed at 3000 cycles per minute, in kW.
d)    the thermal efficiency.
e)    the mean effective pressure, in kPa.
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Expert Answer

Step 1

Part(a).

Given:

Compression ratio = 9.1

Vd = 2.2L

P1 = 95kPa

T1 = 290K

Qtotal = 4.5kJ

Step 2

Solution:

T1=290K

T2=701.51K

T3=1423.6K

T4=2971.8K

T5=1561.9K

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QIca45k On substituting the values, - toat 1.125(0.00217) (0.718) (7 - 701.51K) 4.5 1.125k 4 T 1423.6K giventhat Q3.375KJ 3.375kJ mC (T-T;) 3.375 0.00217x1.005 x(7-1423.6) 3 x4.5 3.375kJ 4 Q34= 2.2L 0.0022m3 Now T 2971.8K Again Finding PV_PV T3 4 m T T V. =4:constant pressure T T T 290x (9.1) T290x (9.1) T 290x 2.419= 701.51K 14-1 0.002472-0.0022 2971.8 1423.6 V = 0.0005m2 So QmC, (7-7) Q3s= mC, (T-701.51K) k-1 4 T T V 1.4-1 0.0005 T 2971.8 0.002472 T 2971.8(0.2022)* = 2971.8x0.5276 T 1561.9K

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Step 3

Part (b):

Net work of the c...

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ΣW-Σ ,-Σ9 ΣW-4.5 -mC, (T -1) ΣW-4.5 -0.00217 x0.71x 1271.9 ΣW-4.5-1.98 ΣW =2.52Uper wcle

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