\input{labpreamble}
\begin{document}
\subsubsection*{PHSX 101L\hfill Experiment 8\hfill Name:\underline{\hspace*{2in}}}

\underline{Title:} Thermal Equivalent of Mechanical Work

\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.

\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.

Other forms of energy can be transformed into thermal energy, such as when 
mechanical work is done against a frictional force.  Historically the 
unit of measure for thermal energy 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).

Thus, if thermal energy 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 thermal energy (so use grams for $m$ and 
\degree C for $\Delta T$).
\begin{eqnarray}
\label{joule}({\rm work\ in\ joules})&=&({\rm thermal\ energy\ in\ calories})\\
({\rm force\ in\ newtons})({\rm distance\ 
in\ meters})&=&({\rm specific\ heat})({\rm mass})({\rm 
temperature\ rise})
\end{eqnarray}


\underline{Procedure:} 
The apparatus 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, and the 
number of turns is counted.  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 embedded 
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.

\underline{Apparatus:} Draw a diagram of the apparatus used. 
\vspace{1.8in}
\goodbreak

\vspace{-.2in}
\underline{Results:} \hfill Trial 1 \hspace{1.2in} Trial 2 \hspace{.3in}
\vspace{-.1in}

\begin{enumerate}

\item
Specific heat of aluminum:\ \underline{\hspace{1.2in}}

\item
Mass of aluminum cylinder:\ \underline{\hspace{1.2in}}

\item
Initial resistance: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Final resistance: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Initial temperature: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Final temperature: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Thermal energy generated (in calories): \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\hrulefill
\vspace{.05in}

\item
Mass hanging on cord:\ \underline{\hspace{1.2in}}

\item
Weight of hanging mass:\ \underline{\hspace{1.2in}}

\item
Cylinder: Dia.:\ \underline{\hspace{.9in}}\ \ Circumf.:\ \underline{\hspace{.9in}}

\item
Number of revolutions: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Total distance: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item
Work done (in joules): \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\hrulefill
\vspace{.05in}

\item
Time spent cranking: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item\label{expt}
Joules per calorie found here: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\item\label{theory}
Accepted value for joules per calorie:\ \underline{\hspace{1.2in}}

\item
Percent difference between \ref{expt} and \ref{theory}: \hfill \underline{\hspace{1.2in}}\hspace{.5in}\underline{\hspace{1.2in}}

\end{enumerate}


\underline{Questions:} 
\vspace{-.25in}
\begin{enumerate}
\item What technique did you use to minimize thermal energy loss or gain from 
the room?  Did trial 2 yield a better result than trial 1?  Why or 
why not?
\vspace{.3in}

\item Approximately what power (in watts) was provided by the person 
turning the crank?
\vspace{.3in}

\item How long would it take to heat water for a bath using this 
technique?  (Assume 40 liters of water being heated from 15$^{\circ}$C to 39$^{\circ}$C.)

\end{enumerate}

\underline{Conclusions:} 


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