Formula: Entropy Change Due to Pressure Change Entropy Amount of substance Gas constant Pressure
$$\mathit{\Delta} S ~=~ n \, R \, \mathrm{ln}\left( \frac{ \class{blue}{\mathit{\Pi}_2} }{ \class{red}{\mathit{\Pi}_1} } \right)$$
$$\mathit{\Delta} S ~=~ n \, R \, \mathrm{ln}\left( \frac{ \class{blue}{\mathit{\Pi}_2} }{ \class{red}{\mathit{\Pi}_1} } \right)$$
$$n ~=~ \frac{\mathit{\Delta} S}{R} \, \mathrm{ln}\left( \frac{ \class{red}{\mathit{\Pi}_1} }{ \class{blue}{\mathit{\Pi}_2} } \right)$$
$$R ~=~ \frac{\mathit{\Delta} S}{n} \, \mathrm{ln}\left( \frac{ \class{red}{\mathit{\Pi}_1} }{ \class{blue}{\mathit{\Pi}_2} } \right)$$
$$\class{red}{\mathit{\Pi}_1} ~=~ \class{blue}{\mathit{\Pi}_2} \, \mathrm{e}^{-\frac{\mathit{\Delta} S}{n\,R}}$$
$$\class{blue}{\mathit{\Pi}_2} ~=~ \class{red}{\mathit{\Pi}_1} \, \mathrm{e}^{\frac{\mathit{\Delta} S}{n\,R}}$$
Entropy change
$$ S $$ Unit $$ \frac{\mathrm J}{\mathrm K} = \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$
The entropy change \( \Delta S = S_2 - S_1 \) of an ideal gas from the initial value \(S_1\) to the final value \(S_2\).
Amount of substance
$$ n $$ Unit $$ \mathrm{mol} $$
The amount of substance \(n\) indicates the number of particles (atoms, molecules, or ions) in a substance. It is defined as the ratio of the particle count \( N \) to the Avogadro's constant \( N_{\text A} = 6.022\,140\,76 \cdot 10^{23} \, \frac{1}{\mathrm{mol}} \):
$$ n ~=~ \frac{N}{N_{\text A}} $$
In one mole of a substance, there are approximately \(6 \cdot 10^{23}\) particles.
Gas constant
$$ R $$ Unit $$ \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$
Molar gas constant (also called universal gas constant) is a physical constant from thermodynamics and has the following exact value:
$$ R ~=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$