# What process is it when the polytropic index $n$ is equal to $- \infty$?

From $$Pv^n = \mathrm{constant}$$ When $$n = - \infty$$ What kind of process is it.... Eg... When $$n= \infty$$, It is constant volume....

Therefore when $$n =- \infty$$... What is constant?

• Is this a serious question or is it an "I was just wondering" question? – Chet Miller Mar 16 at 11:37
• Hi Chimaobi, welcome to the Physics SE. Please use the MathJax syntax for your math expressions to make them better readable. – flaudemus Mar 16 at 14:20

\begin{align} P v^{-\infty} &= K \\ \frac{P}{v^\infty} &= K \\ \frac{v^\infty}{P} &= \frac{1}{K} \\ v^\infty\frac{1}{P} &= \underbrace{\frac{1}{K}}_{K'} \end{align} Variations in $$v$$ get scaled by an exponent of $$\infty$$ and are therefore infinitely more important in determining whether the result is $$K'$$ than variations in $$1/P$$ are. The process is still constant volume.