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Thermodynamics: polytropic processes

  • Thread starter silentwf
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  • #1
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Homework Statement


"During some actual expansion and compression processes in piston-cylinder devices, the gases have been observed to satisfy the relationship [tex]PV^n=c[/tex] where n and C are constants. Calculate the work done when a gas expands from 150kPa and .03 m^3 to a final volume of .2m^3 for the case of n = 1.3


Homework Equations


[tex]W = \int_{1}^{2} {P}dV[/tex]


The Attempt at a Solution


[tex]PV^n=C \Rightarrow P=CV^{-n} \Rightarrow
W = \int_{.03}^{.2} {150V^{-1.3}}dV = 621 kJ[/tex]
Which...is wrong :(

The solution the book offers is:
[tex] P_{2} = P_{1}\frac{V_{1}}{V_{2}}^n = (150)\frac{.03}{.2}^{1.3} = 12.74 kPa
\Rightarrow W = \int_{1}^{2} {P}dv = \frac{P_{2}V_{2} - P_{1}V_{1}}{1-n}
=\frac{(12.74 \cdot .2 - 150 \cdot .03)}{1-1.3} = 6.51 kJ[/tex]

Could someone explain why the way i did it is "unacceptable"?
 
Last edited:

Answers and Replies

  • #2
Mapes
Science Advisor
Homework Helper
Gold Member
2,593
17
Because [itex]C\neq150[/itex]; check your integrand.
 
  • #3
37
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Oh...woops
I put in 150 cuz i was still thinking that [tex]W = P\Delta V[/tex] and I put in 150
then what would i put in? the question does not supply C though
 
  • #4
Borek
Mentor
28,298
2,683
You can calculate C from initial state.

--
methods
 
  • #5
37
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oh lol!
ok, i got the answer, thanks :)
 

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