Carbon dioxide (CO2) gas in a piston-cylinder assembly undergoes three processes in series that begin and end at the same state
(a cycle).
Process 1-2: Expansion from State 1 where p1 = 10 bar, V1 = 1 m3 , to State 2 where V2 = 4 m3 . During the process, pressure and volume are related by pV1.5 = constant.
Process 2-3: Constant volume heating to State 3 where p3 = 10 bar.
Process 3-1: Constant pressure compression to State
Sketch the processes on p-V coordinates and evaluate the work for each process, in kJ. What is net work for the cycle, in kJ?
Process 1-2: Expansion from State 1 where p1 = 10 bar, V1 = 1 m3 , to State 2 where V2 = 4 m3 . During the process, pressure and volume are related by pV1.5 = constant.
Process 2-3: Constant volume heating to State 3 where p3 = 10 bar.
Process 3-1: Constant pressure compression to State
Sketch the processes on p-V coordinates and evaluate the work for each process, in kJ. What is net work for the cycle, in kJ?
1 answer:
Answer:
a) W =400 kJ
b) W = 0 kJ
c) W =-160.944 KJ
Explanation:
Given
Process 1 ---> 2
Pressure at point (1) P1 = 10 bar = P2
Volume at point (1) V1 = 1 m^3
Volume at point (2) V2 =4 m^3
For Process 2 ---> 3, where V = constant
Pressure at point (3) P3 = 10 bar
Volume at point (3) V3 = 4 m^3
Process 3 ---> 1 defined as PV = constant.
Required
Sketch the processes on the PV coordinates To calculate the work in kJ
Work is calculated by W=
a=V2
b=V1
x=Pdx=dV
For Process 1 ---> 2 where P3 = P4 = 5 barW=
a=V3
b=V2x=4dx=dV
substituting the values here into the integral givesW=400 kJFor Process 2 ---> 3
As V = constant in this case, the volume remains unchanged, resulting in W = 0 kJ
For Process 3 ---> 1 By applying point (1) --> 5 x.2 = C ---> C = 1 P = 5V^-1
W=a=V1
x=1V^-1dx=dVsubstituting values into this integral results in
W=| ln V | limits a and b= -160.944 KJ
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