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# There's some rule/mathematical trickery going on here..

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$$\frac{{P}_{i}}{{P}_{f}}= \frac{{V}_{f}}{{V}_{i}}^\gamma$$

$$\frac{{P}_{i}}{{P}_{f}}^{1/2} = \frac{{V}_{f}}{{V}_{i}}$$

I was hoping someone might be able to tell me how they've done this or the rule to use etc

Thanks,

Sonicmaths  May 28, 2017
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Is this in the context of the physics of ideal gases?

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#2
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yes however, my question applies to mathematical rules.

Sonicmaths  May 28, 2017
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In an isentropic process we have   $$\frac{P_i}{P_f}=(\frac{V_f}{V_i})^\gamma$$.

This becomes  $$(\frac{P_i}{P_f})^\frac{1}{\gamma}=\frac{V_f}{V_i}$$    .

Your original would only be valid if   $$\gamma=2$$

.

Alan  May 28, 2017

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