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Polytropic index x is given by
$$\frac{\log \left( \frac {p_2}{p_1}\right)}{\log \left( \frac {v_1}{v_2}\right)}$$
$$\frac{\log \left( \frac {p_1}{p_2}\right)}{\log \left( \frac {v_1}{v_2}\right)}$$
$$\frac{\log \left( \frac {v_1}{v_2}\right)}{\log \left( \frac {p_2}{p_1}\right)}$$
$$\frac{\log \left( \frac {v_2}{v_1}\right)}{\log \left( \frac {p_2}{p_1}\right)}$$
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