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oneosix
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Homework Statement
Horizontal frictionless cylinder piston device- piston is forced againtst a spring which exerts a force directly propotional to the gas volume. Patm (101.13KPa) also acts on the outer face. Considering the gas as a system, calculate the work for the process from an initial state of 200Kpa, 0.1m^3 to a final volume of 0.3m^2. If the spring is taken as a system find the work for the same process.
Homework Equations
Work on spring=1/2kx^2
F=PA
W= integral(PdV) (sorry don't know proper equation tools)
PV/T= constant
The Attempt at a Solution
I must be missing something easy, because it doesn't seem like enough info is given.
Anyway
let x=distance the piston moves
V1= Ah = .1
V2=A(h+x)= .3
rearrange gives x=2h
sum of forces=0 at each state (can i do this?)
P1.A= Patm.A+kh
P2.A= Patm.A+k(h+x)
these 2 eqns gives: kx=P2.A-P1.A
use Work on spring:
W= .5*kx*x
W= .5*(P2.A-P1.A)*2h
use Ah=V1
W= P2.V1-P1.V1
this is as far as i have been able to get and i don't even know if I am on the right track. It appears i need to calculate final pressure, but I'm unsure how. the answers are given which are 59.74 and -39.48 so have thought about working backwards, but don't know how to go about it
Any help is greatly appreciated
(edited: typos)