I have




Where $V=\text{volume}, \ P=\text{pressure} , \ T=\text{temperature},$ $f=\text{number of degrees of freedom per molecule}$ and $\gamma=\frac{f+2}{f}.$

I want to derive $(2)$ from $(1)$

Using the ideal gaslaw I have $T=\frac{PV}{Nk}$, where $N$ and $k$ are constant. Plugging this into $(1)$ I get


and a constant times a constant is constant so finally


However my exponent is off, the denominator in the exponent should be $f$ but I get $2$. What am I missing?

  • $\begingroup$ Please state reason for downvote. $\endgroup$ – Parseval Sep 11 '19 at 14:52
  • $\begingroup$ Seems to be a very 'silly' question; if not question, atleast your response to my answer is not genuine $\endgroup$ – Tojrah Sep 13 '19 at 12:26

You did not put $P^{f/2}$ after the first step. From there you will get the right answer (then you will take both sides of the equation to the 2/f power).

  • $\begingroup$ Please see my response to the answer above, from Tojrah. $\endgroup$ – Parseval Sep 11 '19 at 14:03
  • $\begingroup$ @Parseval You asked what you are missing, you want the whole rest of the derivation worked out? I edited with the next step. $\endgroup$ – user234190 Sep 11 '19 at 14:23

$$V\bigg(\frac {PV}{Nk} \bigg)^{f/2}=\frac{P^{f/2} V^{1+f/2}}{constant}$$

  • $\begingroup$ $P$ is not supposed to have any exponent in the final answer. $\endgroup$ – Parseval Sep 11 '19 at 13:59

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