Entropy- Judge my knowledge [closed]








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Entropy? — So basically I’ve been trying to understand what it is and what I’ve come to realize is. Entropy basically is energy dissipated. What I mean is this — so we know what enthalpy is — it measures the useful energy in the inicial state and in the final state. Heat — measures the energy being transfered during the process, as such, it’s the total energy. Entropy — consists of the amount of energy that was dispersed. As such we can say that a spontaneous reactions occurs, when the entalpy variations, [useful energy] is higher than the energy dissipation [entropy] can we not?




Your idea of energy dispersal is heading in the right direction


Entropy is a thermodyanmic potential describing the distribution of energy states available to the system. 


Assuming that there is a finite number of degenerate (equivalent energy) states $\Omega$, then the absolute entropy $S$ of a system is:


$$S= k\_\mathrm{B} \ln \Omega$$


where $k\_\mathrm{B}$ is the Boltzmann constant.


Let's consider a very simple system of some particles in a fixed volume. If there are four spots that particles can occupy, we can construct states and count them. 


In the case where there are no particles, there is only one state:


$$\begin{array}{|c|c|}\hline
\ &\ \\ \hline
\ &\ \\ \hline
\end{array}\\
S=k\_\mathrm{B} \ln 1 = 0$$


When there is one particle $x$ in the system, there are four states:


$$\begin{array}{cccc}
\begin{array}{|c|c|}\hline
x &\ \\ \hline
\ &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &x \\ \hline
\ &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &\ \\ \hline
x &\ \\ \hline
\end{array} &
\begin{array}{|c|c|}\hline
\ &\ \\ \hline
\ &x \\ \hline
\end{array} 
\end{array}\\
S=k\_\mathrm{B} \ln 4$$


When there are two particles there are twelve states (we have to pretend the two particles are different to get there: $x\_1$ and $x\_2$)


$$\begin{array}{cccc}
\begin{array}{|c|c|}\hline
x\_1 & x\_2 \\ \hline
\ &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
x\_2 & x\_1 \\ \hline
\ &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
x\_2 &\ \\ \hline
x\_1 &\ \\ \hline
\end{array} &
\begin{array}{|c|c|}\hline
x\_2 &\ \\ \hline
\ &x\_1 \\ \hline
\end{array} \\
\begin{array}{|c|c|}\hline
x\_1 &\ \\ \hline
x\_2 &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &x\_1 \\ \hline
x\_2 &\ \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &x\_2 \\ \hline
x\_1 &\ \\ \hline
\end{array} &
\begin{array}{|c|c|}\hline
\ &x\_2 \\ \hline
\ &x\_1 \\ \hline
\end{array} \\
\begin{array}{|c|c|}\hline
x\_1 &\ \\ \hline
\ &x\_2 \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &x\_1 \\ \hline
\ &x\_2 \\ \hline
\end{array} & \begin{array}{|c|c|}\hline
\ &\ \\ \hline
x\_1 &x\_2 \\ \hline
\end{array} &
\begin{array}{|c|c|}\hline
\ &\ \\ \hline
x\_2 &x\_1 \\ \hline
\end{array} \\
\end{array}\\
S=k\_\mathrm{B} \ln 12$$


For similar reasons, three particles would generate 24 states, and so would four particles. When we get to bigger systems (especially macro systems), include different types of particles and interactions between particles, the situation gets more complex, but there are statistical methods that can handle it. 


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