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1 month ago

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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?

1 answer:

inna [3.1K]1 month ago

5 0

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 bar

$\int\limits^a_b {x} \, dx$ W=

a=V3

b=V2

x=4dx=dV

substituting the values here into the integral gives

W=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 $\int\limits^a_b {x} \, dx$

b=V3

x=1V^-1dx=dVsubstituting values into this integral results in

W=| ln V | limits a and b

= -160.944 KJ

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