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\centerline{\textbf{Al}}
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For each of the following statements, work out in your group whether
it is \emph{never true}, \emph{sometimes true} or \emph{always true}.
Explain why your answer is correct, being specific about what
fundamental laws are responsible.  If it is only sometimes true, try to
give examples of each case.

\paragraph{Hot object in cool water}
If I put a hot object (of any material) into a tub of colder
water without changing its pressure:
\begin{enumerate}
\item The temperature of the object will decrease.
\item The internal energy of the object will decrease.
\item The entropy of the object will decrease.
\item The volume of the object will decrease.
\item The entropy of the object plus the entropy of the water will
  increase.
\end{enumerate}

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\paragraph{Identical objects} Consider two identical objects $A$ and $B$, which
could be of any material, and are of the same mass, but are subject to
different conditions (pressure, temperature).
\begin{enumerate}
\item If $A$ has higher volume than $B$, then $A$ has higher entropy.
\item If $A$ has higher temperature than $B$, then $A$ has higher
  internal energy.
\item If $A$ has higher temperature than $B$, but they have the same
  volume, then $A$ has higher internal energy.
\item If $A$ has higher temperature than $B$, but they have the same
  pressure, then $A$ has higher internal energy.
\item If $A$ has higher temperature than $B$, but they have the same
  pressure, then $A$ has higher enthalpy.  ($H = U + pV$)
\item If $A$ has higher temperature than $B$, but they have the same
  pressure, then $A$ has higher entropy.
\end{enumerate}

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\paragraph{Bag of hot air?} Consider an insulated spherical bag full
containing a fluid---which could be either liquid or solid.  The bag
is very strong, so it cannot be stretched, and also happens to be an
excellent thermal insulator.
\begin{enumerate}
\item If I sit on the bag, it will no longer be spherical.
\item If I sit on the bag, the pressure of the bagfull of fluid will
  increase.
\item If I sit on the bag, the volume of the bagfull of fluid will
  increase.
\item If I sit on the bag, the temperature of the bagfull of fluid
  will increase.
\item If I sit on the bag, the entropy of the bagfull of fluid will
  increase.
\item If I sit on the bag, the internal energy of the bagfull of fluid
  will increase.
\item If I sit on the bag, the enthalpy of the bagfull of fluid will
  increase.
\item If I sit on the bag, the Helmholtz free energy of the bagfull of
  fluid will increase.
\end{enumerate}

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\paragraph{Aluminum balloon?} Consider a similar spherical bag that is
an excellent thermal conductor.  In this problem, assume that my
bottom is at room temperature---perhaps because I'm wearing asbestos
undergarments.
\begin{enumerate}
\item If I sit on the bag and wait a while, it will no longer be
  spherical.
\item If I sit on the bag and wait a while, the pressure of the
  bagfull of fluid will increase.
\item If I sit on the bag and wait a while, the volume of the bagfull
  of fluid will increase.
\item If I sit on the bag and wait a while, the temperature of the
  bagfull of fluid will increase.
\item If I sit on the bag and wait a while, the entropy of the bagfull
  of fluid will increase.
\item If I sit on the bag and wait a while, the internal energy of the
  bagfull of fluid will increase.
\item If I sit on the bag and wait a while, the enthalpy of the
  bagfull of fluid will increase.
\item If I sit on the bag and wait a while, the Helmholtz free energy
  of the bagfull of fluid will increase.
\end{enumerate}

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

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