[NOTES/SM-01007]Important Concepts and Results from Thermodynamics

Thermodynamics is based on four laws which are very general and applicable to large variety of systems and have been formulated based on experience.

1. Zeroth law of thermodynamics.
   • Concept of temperature\\ Equation of can be defined as $f(X,Y,T)=0$
2. First Law of Thermodynamics.
   • Internal energy $dQ=dU+dW$\\ $dU=dW$ (adiabatic process)
   • Conservation of energy\\ Heat and work are a ``form'' of energy
3. Second Law \\ Entropy $\oint \frac{dQ}{T}=0$ \\ \textit{reversible process} \begin{align*} \int \frac{dQ}{T}& = S_2-S_1\\ Tds & = dQ \end{align*} Combined Ist and IInd Law $$ TdS = DU+dW \qquad\qquad P,V\Rightarrow \text{coordinates} $$

In equilibrium $P,V,T(X,Y,T)$ are related by equation of state. Any two of these can be chosen as independent variables. \begin{align*} \left. \begin{aligned} S=&S(P,V)\\ U=&U(P,V) \end{aligned}\right\} \qquad \text{Functions can be regarded as coordinates of system} \end{align*} Thermodynamics introduces many other quantities \begin{align*} \left. \begin{aligned} \text{Entropy} &H\\ \text{Free energy}&F\\ \text{Gibbs energy} &G \end{aligned}\right\} \qquad \text{in terms of entropy and coordinates} \end{align*} Equilibrium properties of thermodynamic systems can be described by these functions.