Explanation of how the following calculus work

[maali5]

Homework Statement

The following data has been collected:

Gas volume: V = 0.8 m3
Gas pressure: p = 160 kPa
Compression index: n = 1.4
Pressure/volume relationship: pV^n = C

Work done = ∫ TOP=V2 BOTTOM =V1

You first need to work out C, the value of the pressure/volume relationship.
Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:
integral calculus Simpson’s rule

Comment on the accuracy of the numerical method.
Note: if you wish, you may use a spreadsheet for the numerical method.

3. The Attempt at a Solution

As i did not understand the question, I copied out all the work from a classmate. Would you please explain to me what is going on please.

ThanksPart 1
Integral calculus:

pV^1.4=C so p=C/V^1.4.
Work done ON the gas = -∫p dV = C∫ (1/V)^1.4 dV
= -C [ 1/(-1.4+1)][V^(-1.4+1)]
= -C [ 1/(-0.4][V^(-0.4)]
= +2.5C (1/V2^0.4 - 1/V1^0.4)

V1=0.8, V2=0.6, C=p1V1^1.4=160000*0.8^1.4=117070.

work done = +2.5*117070*(1/0.6^0.4 - 1/0.8^0.4) = +39025 J = +39.0 kJ.
Part 2: Simpson rule - I have attached an excel file I basically don't understand how "group c" includes this formula

This formula being "(117.07*10^3)/(number^1.4) "

for 1= 0.8 =(117.07*10^3)/(0.8^1.4) = 159999,8725
2=0.775 =(117.07*10^3)/(0.775^1.4) =167271,9943

etc
Thank you very much

 

[HallsofIvy]

I really have no clue what you are asking. Under problem statement, you give several formulas (including "Work done = ∫ TOP=V2 BOTTOM =V1" which makes no sense because you don't say what you are integrating) but you don't state what the problem is. Your attachment is just a list of numbers with, again, no statement as to what you are trying to do. I would guess that you are trying to find "work done" but "work done" while doing what?

 

[maali5]

I did not know how to construct a formula. So I have attached the questions below and hopefully you will understand it better.

Thanks

 

[maali5]

Anyone! Just a small explanation will do

 

[Ray Vickson]

Anyone! Just a small explanation will do

You have a relationship between p and V involving a constant C; you also have numerical values of p and V at one point, so you can figure out what must be the value of C. Then you are given an integral ∫ p dV to evaluate. You are even given some hints about Simpson's rule, etc, for finding approximate values of the integral (although in this case the integral is so easy that you can do it directly). So, what is stopping you from actually DOING all this?

RGV

 

[maali5]

Is my english really that difficult to understand?

I have already completed the work just wanted some guidance on how this number came about.

 

[vela]

It's not a question of understanding your English. It's trying to understand what is confusing you when the all of the work is right in front of you. You already admitted you didn't actually do the work yourself and simply copied it from a classmate. The least you can do is put some minimal effort into figuring out what was done.