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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"?

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