A mass of 1.5 kg of air enters a combustion chamber at atmospheric conditions of

Question

A mass of 1.5 kg of air enters a combustion chamber at atmospheric conditions of 100 kPa and 25 degreeC, corresponding to state 1 in the P - v diagram in Figure 3. From state to state 2 the air is compressed to 1/20 of its initial volume during a polytropic process with n = 1.4, requiring J of work. The air is then isobarically heated to 2200 degreeC at state 3, followed by a polytropic expansion with n =1.4 until reaching a pressure of 362.64 kPa at state 4. Finally, the air is isochorically cooled, returning to its initial state. Find the net work produced by this cycle, assuming the air behaves as an ideal gas.

Explanation / Answer

for process 1-2 : (P1V1)^1.4=(P2V2)^1.4 and V2=(V1/20) which gives P2=6628.9 KPA

ALSO W= (P2V2-P1V1)/n-1 which gives V1=1.28 AND V2= .0642

T2=T1(V1/V2)^.4 which provide T2= 987.7 K

for process 2-3: T3/T2=V3/V2 which gives V3=.16 so W=P2(V3-V2) which provides W=635.04

for process 3-4 : W=(P3V3-P4V4)/(n-1) which gives W=1491.112 since V1=V4 and P2=P4

for process 4-1 : W=0 since isochoric

so total workdone by the system in this case= (-742.36+ 635.04+ 1491.112+0 ) = 1383.79 KN-m

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