- #1

fluidistic

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## Homework Statement

The first problem in the book reads:

A given system is such that quasi-static adiabatic change in volume at constant mole numbers is found to change the pressure in accordance with the equation [itex]P= KV^{-5/3}[/itex] where K is a constant.

Find the quasi-static work done on the system and the net het flux to the system in each of the 3 processes indicated in the figure. Each process is initiated in the state A, with a pressure of 32 atm and a volume of 1 liter, and each process terminates in the state B, with a pressure of 1 atm and a volume of 8 liters.

Process a: The system is expanded from its original to its final volume, heat being addd to maintain the pressure constant. The volume is then kept constant and heat is extrated to reduce the pressure to 1 atm.

(I might describe the other processes, only if I have troubles in doing them later)

## Homework Equations

[itex]dW=-PdV[/itex]

[itex]dQ=dU+PdV[/itex]

Answer is W=-224 liter-atm and Q=188 liter-atm.

## The Attempt at a Solution

I tried to use the fact that [itex]P= KV^{-5/3}[/itex], integrated dW from A to D. This gave me [itex]\frac{3}{2}K(8^{-2/3}-1)[/itex]. So I'd get an answer depending on K which isn't acceptable apparently.

Another try was to write [itex]W=-\int _A ^D PdV-\int _D ^B PdV=-P(V_D-V_A)-\int _D ^B PdV[/itex] but in the last integral P decreases at a constant volume so it's not a function of V. I don't know how to perform such an integration.

P.S.:I don't think the figure is required to understand the situation. It is what the problem statement is.

Thanks for any help.