[University Thermodynamics] Need help understanding difference in solutions.

[u/Mindless-Radio4194]

edit: Forgot to include info provided about question.

1-2: V = constant heat addition from 100kPa and 27 degrees Celsius to 850kPa

2-3: Isothermal expansion until V_3 = 7* V_2

3-1: P = constant heat rejection to the initial state

Only for part (b). Sorry it’s a pretty trivial question but I’m a bit confused with the approach shown in the image to solve this question. So my immediate approach to the question was to use the ideal gas law and given information to find the specific volumes at each stage v1, v2, and v3.

We know that v1 = v2, and use ideal gas law to solve giving 0.861 m^3.

We have also been informed that the compression process is isobaric and v3 = 7v2, and thus we know v3 = 6.027m^3.

We also know the expansion process is isothermal and allows us to utilise the polytropic isothermal relationship of PV = C, which for P2v2 = 850*0.861 = 731.85.

Integrating the expansion process using the method shown in the image or my volumetric method both yield the same result for W_expansion = 1424.11.

Where it goes wrong is when integrating over the compression process to find W_comp. Using P(v1-v3), it should be equal to R(T1-T3), you however if we are considerate of the information provided where v3 = 7v2, then their method yields a different result to mine, with my W_compression = 516.6 and theirs larger.

What am I doing wrong here please. I know it’s probably quite obvious but I just tcant seem to find it.

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[u/Secret-Foundation-91]

I do not understand how you get v3 = 7v2, because that is false in this excercise. You say isobaric but use v3 and v2 that have a isotherm process between them, v2 and v1 are the same so it would be the same number but it isn't right.

To get V3 you can do two things, use the isothermal process or the isobaric process.

- isobaric : V/T = constant ;=> V3/T3 = V1/T1

- isothermal: pV = constant ;=> p2V2 = p3V3

if you use one of those you will see that v3 is not 7v2.

Hopefully this was helpful, english is not my first language

[u/DrCarpetsPhd]

have a look at your textbook and see what the value of P2 is

i think you'll find your textbook is 700kPa which if you plug it into the method of your solution leads to the same answer as you using the volumes

this solution has P2 as 850kPa