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\centerline{\textbf{Ungraded Quiz}}
\bigskip

\noindent
Consider the two processes described below.
\paragraph{Process \#1} Five moles of an ideal gas are initially
confined in a one-liter cylinder with a movable piston, at a
temperature of 300~K.  Slowly the gas expands against the movable
piston, while the cylinder is in contact with a thermal reservoir at
300~K.  The temperature of the gas remains constant at 300~K while
the volume increases to two liters.
\paragraph{Process \#2} A thin plastic sheet divides an insulated
two-liter container in half.  Five moles of the same ideal gas are
confined to one half of the container, at a temperature of 300~K.
The other half of the container is a vacuum.  The plastic divider is
suddenly removed and the gas expands to fill the container.  Because
it is a free expansion of an ideal gas (no work is done on or by the
gas), the final temperature of the gas is also 300~K.
\paragraph{Process \#3} The same cylinder as in process \#1 is
thermally insulated and then allowed to slowly expand, starting at
300~K, to twice its original size (two liters).
\begin{center}
  \includegraphics[width=\columnwidth]{eefree_expansionfig.png}
\end{center}
\begin{enumerate}
\item Are $\Delta S_\text{isothermal}$, $\Delta S_\text{free}$ and
  $\Delta S_\text{adiabatic}$, the change in entropy of the gas for
  each process, positive, negative, or zero?  Please explain your
  reasoning.
  \vfill
\item Is $\Delta S_\text{isothermal}$ greater than, less than, or
  equal to $\Delta S_\text{free}$?  How do each of these compare
  with $\Delta S_\text{adiabatic}$? Please explain.
  \vfill
\item Are $\Delta S_\text{surr-isothermal}$, $\Delta
  S_\text{surr-free}$ and $\Delta S_\text{surr-adiab}$, the change
  in entropy of the surroundings for each process, positive,
  negative, or zero?  Please explain.
  \vfill
\end{enumerate}

\vfill
\leftline{\textit{by David Roundy}}
\leftline{\copyright DATE David Roundy}

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