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mass of 4 kilograms of carbon dioxide (CO2) in a piston-cylinder assembly undergoes two processes in series from an initial state where p1 = 0.5 MPa, T1 = 267°C: Process 1–2: Constant-temperature expansion until the volume is twice the initial volume. Process 2–3: Constant-volume heating until the pressure is again 0.5 MPa. Assuming ideal gas behavior, determine the overall work, in kJ.

Answer :

Olajidey

Answer:

The over all work done is 141.4kJ

Explanation:

Given that,

p1 = 0.5 MPa

T1 = 267°C

Calculate the gas costant of cardondioxide

[tex]R = \frac{8.314}{ Molar .mass} \\\\[/tex]

[tex]R= \frac{8.314}{44} \\\\= 0.1889kJ/kg.k[/tex]

Calculate the work done during the process 1-2

[tex]W_1-_2 = p_1v_1 In\frac{v_2}{v_1}[/tex]

          [tex]= mRTIn\frac{v_2}{v_1}[/tex]

[tex]2 \times 0.1889 \times (267 + 273)In\frac{2v_1}{v_1} \\\\= 141.4kJ[/tex]

Considering that the process 2-3 is constant volume process,

hence the work done is zero

[tex]W_2 - _3 = 0[/tex]

Calculate the over all work done

[tex]W = W_1-_2 + W_2-_3\\ W = 141.4kJ + 0\\W = 141.4kJ[/tex]

The over all work done is 141.4kJ

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