Work done by gases in an internal combustion engine expansion

[eku_girl83]

Here's my problem:
Measured data for pressure versus volume during the expansion of gases within the cylinder of an internal combustion engine are given in the table below.
Data Point p (bar) V (cubic cm)
1 15 300
2 12 361
3 9 459
4 6 644
5 4 903
6 2 1608

A) Determine a value of n such that the data are fit by an equation of the form p*(V^n)=constant
I got n=1.205559 and constant=14534.734
So p=14534.734/(V^1.205559)

B) Evaluate analytically the work done by the gases, in KJ.
I integrated 14534.734/(V^1.205559) with respect to V and evaluated with limits of 300 and 1608 (smallest and largest values for volume). I got 6389.453

*Question: What units should this be in? I know it's not in KJ, as the original data is in bars and cubic centimeters. How and where do I convert to get an answer in kJ?

Any help would be greatly appreciated!

 

[Integral]

A separate issue while I think about the units.

Your data has only 3 significant digits, that is the absolute maximum that should appear in your results. When recording these sort of results you need to learn to ignore the meaningless digits generated by your calculator.

BTW: You have a very good fit to the data using
c= 1.45e4 and n=1.2

 

[Integral]

Ok, ignore the units on the Vⁿ term and consider what the units of the area under the PvsV line must be. Simply multiply the units of the axis. So the area under the curve, regardless of the functional description of the curve must be in Bar*cm³.


Can you do the conversion from there?

 

[eku_girl83]

Thanks for clarifying the units. About the significant figures, I usually carry the numbers out pretty far until I reach the complete end of the problem and then round. Sorry if I made it appear that I write numbers with 10 digits after the decimal as a final answer :)