# Work done on real thermodynamic data

## Homework Statement

I have the data for a p-v diagram from experiment of a fluid (the fluid is unknown). The data is attached below as the crosses. It also has the approximated ideal cycle for that data. Does anyone know how to find the work done for this real experimental data? Maybe a MATLAB command or some other software? Also, would v2/v1 be the compression ratio for this cycle?

## The Attempt at a Solution

I tried using the trapz function in MATLAB however unsure whether it is correct or not.

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Do you know how work is defined as the cyclic integral of P with respect to V? You may very well need to do some numerical integration, and you may (or may not) want to use some interpolation/extrapolation to augment the data to what you think is the true curve in regions that are poorly defined.

Chestermiller
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## Homework Statement

I have the data for a p-v diagram from experiment of a fluid (the fluid is unknown). The data is attached below as the crosses. It also has the approximated ideal cycle for that data. Does anyone know how to find the work done for this real experimental data? Maybe a MATLAB command or some other software? Also, would v2/v1 be the compression ratio for this cycle?

## The Attempt at a Solution

I tried using the trapz function in MATLAB however unsure whether it is correct or not.
Are there analytic expressions fitted to the ideal cycle?

Are there analytic expressions fitted to the ideal cycle?
Yes there are. The power stroke is pv^-1.5=544.7 and the compression process is pv^-1=199.7

Chestermiller
Mentor
Yes there are. The power stroke is pv^-1.5=544.7 and the compression process is pv^-1=199.7
Then you can integrate pdv for each of them from the lowest volume to the highest volume. Those exponents on v are not correct.

Once you assume a functional form, you have abandoned the experimental data for the most part. If we want to work with the experimental data, we should do just that.

Chestermiller
Mentor
Once you assume a functional form, you have abandoned the experimental data for the most part. If we want to work with the experimental data, we should do just that.
I respectfully disagree if the analytic functional form is an excellent fit to the experimental data (as it appears to be in the figure).

It seems that I need to do numerical integration to find the work done for the real data (because I'm specifically told to find the work done from the real data not from the ideal cycle). Does anyone know how to do that in excel say? or does it have to be in MATLAB or some other advanced software?

Aldo, get a calc book or a numerical methods book, and look up "quadrature." You will likely want to look at the Trapezoidal Rule, or possibly Simpson's Rule (the later only if the data are evenly spaced). You can implement these methods in Fortran, BASIC, spead sheet, etc., just about anything that will enable the computer to do a lot of arithmetic for you.

Chestermiller
Mentor
It seems that I need to do numerical integration to find the work done for the real data (because I'm specifically told to find the work done from the real data not from the ideal cycle). Does anyone know how to do that in excel say? or does it have to be in MATLAB or some other advanced software?
Why don't you just use the trapezoidal rule, and compare with the integration of the analytic fits.

Is this homework or a course lab problem? Or is this from an industrial source? How to interpret the rules depends somewhat on the source of the problem.

It's a course lab problem; yea I think I need to go and read a numerical methods book as you said. Thanks for your help

Chestermiller
Mentor
It's a course lab problem; yea I think I need to go and read a numerical methods book as you said. Thanks for your help
Can you please provide the actual p-v data?