Formula Adiabatic Process Pressure before Volume before Adiabatic index Pressure after Volume after
$$\class{red}{\mathit{\Pi}_1} ~=~ \class{blue}{\mathit{\Pi}_2} \, \left(\frac{\class{blue}{V_2}}{\class{red}{V_1}}\right)^{\gamma}$$ $$\class{red}{\mathit{\Pi}_1} ~=~ \class{blue}{\mathit{\Pi}_2} \, \left(\frac{\class{blue}{V_2}}{\class{red}{V_1}}\right)^{\gamma}$$ $$\class{red}{V_1} ~=~ \left( \frac{ \class{blue}{\mathit{\Pi}_2} }{ \class{red}{\mathit{\Pi}_1} } \, {\class{blue}{V_2}}^{\gamma} \right)^{-\gamma}$$ $$\gamma ~=~ \frac{ \ln(\class{red}{\mathit{\Pi}_1}) ~-~ \ln(\class{blue}{\mathit{\Pi}_2}) }{ \ln(\class{blue}{V_2}) ~-~ \ln(\class{red}{V_1})}$$ $$\class{blue}{\mathit{\Pi}_2} ~=~ \class{red}{\mathit{\Pi}_1} \, \left(\frac{\class{red}{V_1}}{\class{blue}{V_2}}\right)^{\gamma}$$ $$\class{blue}{V_2} ~=~ \left( \frac{ \class{red}{\mathit{\Pi}_1} }{ \class{blue}{\mathit{\Pi}_2} } \, {\class{red}{V_1}}^{\gamma} \right)^{-\gamma}$$
Pressure before
$$ \class{red}{\mathit{\Pi}_1} $$ Unit $$ \mathrm{Pa} $$ Pressure of the ideal gas BEFORE the adiabatic process.
Volume before
$$ \class{red}{V_1} $$ Unit $$ \mathrm{m}^3 $$ Volume of the ideal gas BEFORE the adiabatic process.
Adiabatic index
$$ \gamma $$ Unit $$ - $$ Adiabatic index is the quotient of heat capacities at constant pressure \( c_{\small{\Pi}} \) and volume \( c_{\small{\text V}} \).
For example, for monatomic gas: \( \gamma ~=~ \frac{5}{3} \).
Pressure after
$$ \class{blue}{\mathit{\Pi}_2} $$ Unit $$ \mathrm{Pa} $$ Pressure of the ideal gas AFTER the adiabatic process.
Volume after
$$ \class{blue}{V_2} $$ Unit $$ \mathrm{K} $$ Volume of the ideal gas AFTER the adiabatic process.