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\subsubsection*{PHSX 221L\hfill Thermal Equivalent of Mechanical Work\hfill Name:\underline{\hspace*{2in}}}

% \noindent
% \underline{Title:} Thermal Equivalent of Mechanical Work

\noindent
\underline{Object:} To experimentally measure the thermal equivalent 
(in calories) produced by a known amount of mechanical work (in 
joules), and thus calculate the number of joules in one calorie.

\noindent
\underline{Theory:} One of the most important discoveries in the 
history of physical science was the realization that heat was not a 
fluid substance which, when added to a body, would raise its 
temperature.  instead, it is now known that heat is a form of energy 
(thermal energy) that can be transferred from one object to another by 
virtue of a temperature difference.

\noindent
Other forms of energy can be transformed into thermal energy when 
mechanical work is done against a frictional force.  Historically the 
unit of measure for heat has been the calorie (defined as the amount 
of heat required to raise the temperature of one gram of water one 
degree Celsius), but the official unit of mechanical work is the 
joule (defined as the product of one newton of force acting through 
one meter of distance).

\noindent
Thus, if heat is produced by doing work against friction we should be 
able to experimentally determine the work done by measuring the force 
applied and the distance moved.  The product of these two quantities 
will give the number of joules of work, which can then be compared to 
the number of calories of heat:
\begin{eqnarray}\label{joule}
[{\rm work\ (J)}] &=& [{\rm force\ (N)}][{\rm distance\ (m)}]\\ 
\ [{\rm thermal\ energy\ (cal)}]
&=& [{\rm specific\ heat\ (cal/g ^{\circ} C)}][{\rm 
mass\ (g)}][{\rm temperature\ rise\ (^{\circ} C)}]
\end{eqnarray}

\noindent
The work may also be calculated from $W=\tau\theta$ where $\tau = MgR$ 
and $\theta = 2\pi N$.  ($M$ is the mass hanging from the rope, $R$ is 
the radius of the aluminum cylinder.)  This formula is exactly 
equivalent to equation \ref{joule}.

\noindent
\underline{Apparatus:} Draw a diagram of the apparatus used.  It 
consists of an aluminum cylinder around which is wrapped a nylon 
cord.  With a weight hanging on the cord to provide a known tension 
force, the cylinder is rotated by means of a crank.  The frictional 
force created as the cord rubs against the surface of the cylinder 
produces a heating effect, which raises the temperature of the 
aluminum.  A thermocouple imbedded in the aluminum cylinder makes it 
possible to determine the temperature of the cylinder by measuring 
its resistance with an ohmmeter.  From a graph of resistance versus 
temperature, we can determine the cylinder's temperature.

\noindent
\underline{Procedure:} 
\vspace{-.25in}
\begin{enumerate}

\item To estimate the size of some of your error, do the experiment 
twice.  The first time start at room temperature, and the second time 
start the experiment as much below room temperature as you end 
it above.  (Why?)

\item If you also measure the cranking time you can compute the power 
output of the person cranking.

\item Record the number of turns the cylinder must be cranked to give 
a specific rise in the temperature of the aluminum cylinder.  Watch 
for the highest temperature reading (even if it occurs after you stop 
cranking).

\end{enumerate}


\noindent 
\underline{Analysis:}
\vspace{-.25in}
\begin{enumerate}
\item Compare your value of $J$ (work done 
in joules divided by heat produced in calories) with the book value.

\item Compute the average power output of the person cranking.
\end{enumerate}


\noindent
\underline{Conclusions:} 
\vspace{-.25in}
\begin{enumerate}
\item Discuss any sources of error that you feel might have affected 
your results.  Are some of these avoidable?  What effect would they 
have on your value of $J$?  Can you estimate the magnitude of the 
effects?

\item Is it experimentally possible that the heat absorbed by the 
cylinder could be greater than the work performed on it?  Explain.

\end{enumerate}


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