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\centerline{\textbf{Using $pV$ plots}}\normalsize
\medskip
  We'll begin the day by looking at processes that happen at constant
  pressure, volume, temperature or entropy.  This touches on the
  name-the-experiment discussion we had yesterday.

 
  \centerline{\includegraphics[width=5 in]{eepvplotshandfig1.png}}


  We talked about measurements such as
$$
    \left(\frac{\partial \tau}{\partial L}\right)_{S} 
$$
$$
    \left(\frac{\partial L}{\partial T}\right)_{\tau} 
$$

  In these measurements, we measure how a state variable changes as    we vary another one.  Another sort of measurement involves
  \emph{integrals} rather than derivatives, and measures finite
  changes.  To discuss this, it's common to use what are called $pV$
  diagrams.  For instance, consider the diagram above.

  In your groups, work out the following questions:
  
  \begin{enumerate}
  \item What does this describe? Is $p$ a function of $V$?
  \item What is the net work done after one cycle of this
  process? How much work was done at each step?
  \item  What is the net heat transfer over one cycle of this process? For each step?
  \end{enumerate}
  
  \vfill
  \newpage
  \centerline{\includegraphics[width=5 in]{eepvplotshandfig2.png}}

  
  Now let's look at another cycle.  Let's consider the figure above, which looks similar but is a plot of $T$ vs. $S$, and answer the following questions.

  \begin{enumerate}
  \item What is this cycle? How would you go about running a cycle like this?

  \item What is the net heat transfer over one cycle of this process? How much was transfered on each step?

  \item What is the net work done after one cycle of this
  process? How much work was done at each step?
  
  \end{enumerate}
  
  
  \vfill
  \leftline{\textit{by David Roundy}}
  \leftline{copyright DATE David Roundy}
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