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\begin{document}

\frame{\frametitle{\b 2nd Law of Thermodynamics - 1} \medskip

{\bf Compressed Gas (1):} Integrate
$$ \frac{dT}{T} = -\frac{nR}{C_V}\frac{dV}{V}~~{\rm with}~~
   C_V=2.5\,nR\,. $$
\smallskip

{\bf Efficiency of a Heat Engine (2):} $T_h=T_c/(1-ef)$ with h hot,
c cold and ef efficiency.
\bigskip

{\bf Heat Engine (3):} Given is the Power $P$ in units of $W=J/s$,
the efficiency $ef$ and the number of cycles $n_c$ per $s$. . 

1. The work per cycle is then just $W=P\,/\,n_c$.

2. The heat rejected per cycle follows then from $W=ef\,Q_{\rm input}$,
$Q_{rc}=(1-ef)\,Q_{\rm input}=\dots W$.
\bigskip

{\bf Ideal Heat Engine (4):} 1. Work done: $W=ef\,Q_h$ (hot reservoir).

2.~Coefficient of performance of an ideal refrigerator: $cop=Q_c/W$
(cold reservoir).
\vskip 20pt }


\frame{\frametitle{\b 2nd Law of Thermodynamics - 2} \medskip

{\bf Carnot Engine (5).} 1.\ Efficiency $ef=1-T_c/T_h$ (cold/hot).
\smallskip

2.\ Work done: $W=ef\,Q_h$ (per cycle).
\smallskip

3.\ Heat rejected: $Q_r=Q_h-ef\,Q_h$.
\smallskip

4.\ Coefficient of performance: $cop=Q_r/W$.
\vskip 20pt }
\end{document}
