One kmol of carbon monoxide (ideal gas) with a constant pressure heat capacity o
ID: 982802 • Letter: O
Question
One kmol of carbon monoxide (ideal gas) with a constant pressure heat capacity of 29.3 kJ/(kmol-K) undergoes the following process: Carbon monoxide at 2.758 MPa and 700K (state 1) is isothermally expanded to 0.552 MPa (state 2), is isochorically cooled to 437.5 K (state 3), is isobarically cooled to 350 K (state 4), is adiabatically compressed to 2.758 MPa (state 5), and is heated at constant pressure to 700 K. Determine Q, W, Delta H, and Delta U for each step of the process and overall (in kJ), assuming reversibility of the processes]Explanation / Answer
State 2 : For isothermal compression delU= 0 , delH= 0 and W=-nRT ln (P1/P2), Q=-W
W= -1*8.314*700*ln (2.758/0.552)= -9362.4KJoules
Q=-W= 9362.4 joules
Given Cp =29.3 KJ/kmol.K CP-CV= R and CV= CP-R= 29.3-8.314= 20.986 KJ/Kmol.K
State 3 : isohoric process : W= 0, Q= delU=n CV*(T2-T1)= 1*20.986*(437.5-700)=-5508.8 Kj
delH= 1*Cp*(T2-T1)= 1*29.3*(437.5-700)= -7691.25K
for isochoric process P1/T1= P2/T2
P2= P!*T2/T1= 0.552*437.5/700=0.345 Mpa
state4 : isobaric cooling to 350 K, Q= delH= nCP*(T2-T1)= 1*29.3*(350-437.5)=-2563.75 Kj
W=-nR*(T2-T1)=-1*8.314*(350-437.5)= -727.475KJ
delU= n*CV*(T2-T1)= 1*20.986*(350-437.5)=-1836.3 Kj
Step 5:
For adiabatic process Q=0 ,W= nR*(T2-T1)/(Y-1).Y= Cp/CV= 29.3/20.986=1.4
T1= 350 K and T2=T1* {P2/P1(at the end of step4)}R/CP= 350*(2.758/0.345)8.314/29.3 =350*1.8
T2= 630 K W= 8.314*(630-350)/(1.4-1 )=5819.8 Kj
delH = nCP*(T2-T1)= 1*29.3*(650-350)= 8790 Kj
delU= n*Cv*(T2-T1)= 1*20.896*(650-350)=6268.8 Kj
last step : heating at constant pressure to 700K
delU= 1*20.896*(700-650)= 1044.8Kj , Q= delH=1* Cp*(T2-T1)= 1465 Kj
W=-1*R*(T2-T1)=-8.314*50= -415.7Kj
The complete data is represented in the table
State
delU (KJ)
delH (KJ)
Q (KJ)
W(KJ)
State-2
0
0
9362.4
-9362.4
State-3
-5508.3
-7691.25
-5508.3
0
State-4
-1836.4
-2563.75
-2563.75
-727.475
State-5
6268.8
8790.
0
5819.8
State-1
1044.8
1465
1465
-415.7
State
delU (KJ)
delH (KJ)
Q (KJ)
W(KJ)
State-2
0
0
9362.4
-9362.4
State-3
-5508.3
-7691.25
-5508.3
0
State-4
-1836.4
-2563.75
-2563.75
-727.475
State-5
6268.8
8790.
0
5819.8
State-1
1044.8
1465
1465
-415.7
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