\input{labpreamble}
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\begin{document}

\subsubsection*{PHSX 222L\hfill  Specific Heat and Latent Heat\hfill Name:\underline{\hspace*{2in}}}


\underline{Object:} To determine the specific heat of various 
substances and the latent heat of melting for ice.

\underline{Introduction:} \emph{Specific heat}, $c$, is an indication
of how much the temperature of an object will change when internal
energy is increased or decreased.  Specific heat varies from substance to
substance which means that two objects of the same mass but of
different substances will change temperatures by different amounts
when their internal energies are incrased or decreased by the same 
amount.  For example,
have you ever held a hot piece of pizza by its crust only to have the
moister parts burn your mouth when you take a bite?  The meats and
cheeses have high specific heat, while the crust has a low specific
heat.  The specific heat of a substance would be the slope of a
graph of the change in energy  vs.\ the mass of the object times the change in
temperature.  ($E$ has been used for other kinds of energy, so we'll 
use $U$ specifically for internal energy though many textbooks 
use $Q$.)
\begin{equation}\label{c}
	\Delta U= cm\Delta T
\end{equation}
Therefore the specific heat of a substance can be calculated by measuring the 
change in temperature of an object which corresponds to a known change 
in the internal energy of the object (such as by doing mechanical work on the object).

Specific heats of different substances can be compared by measuring
temperature changes as one object heats another.  For example, if a
sample of hot metal is dropped into some cold water then they
both arrive at a common temperature somewhere between the extremes. 
By using a good calorimeter to minimize interaction with the air in the room
we can assume that the decrease in
internal energy of the metal is equal to the increase in internal
energy of the water.
\begin{equation}
	-\Delta U_m=\Delta U_w
\end{equation}
\begin{equation}\label{compare}
	-c_{\rm m}m_{\rm m}\Delta T_{\rm m}=c_{\rm w}m_{\rm w}\Delta T_{\rm w}
\end{equation}

We'll first do some mechanical work on some lead and assume
the work increases the internal energy of the lead, and then use that
assumption to calculate the specific heat of lead.  Then we'll use our
new knowledge (and equation \ref{compare}) to calculate the specific
heat of water; and then use the specific heat of water (and equation
\ref{compare}) to calculate the specific heat of a different metal.

\emph{Latent heat}, $L$, is the amount of energy (per unit mass)
needed to effect a change of state at a constant temperature.  For
example, the latent heat of melting (or fusion), $L_{f}$, for ice is
the amount of energy (per unit mass) needed to change the ice at
0\degree C to water at 0\degree C; the accepted value is 79.8~cal/g. 
Likewise, the latent heat of vaporization, $L_{v}$, for water is the
energy (per unit mass) needed to change the liquid water at the
boiling temperature to the gaseous state at that temperature; the
accepted value is 539~cal/g.  We can modify equation \ref{compare} to
handle a change of state.  Specifically, when ice cubes at 0\degree C
are put in warm water:
\begin{equation}\label{latent}
	-c_{\rm w}m_{\rm w}\Delta T_{\rm w}=m_{\rm ice}(L_{f})_{\rm ice} + 
	c_{\rm melted\ ice}\ m_{\rm ice}\ \Delta T_{\rm melted\ ice}
\end{equation}

\newpage

\underline{Procedure:}  Both lead and mercury are poisonous so don't 
eat the lead and don't break the thermometers.

\underline{Using equation \ref{c}}:
\vspace{-.2in}
\begin{enumerate}
	\item Fill a plastic bottle about 1/4 full of lead shot and find the mass of the lead. 
	\item Measure the initial temperature (in \degree C) of the lead shot 
	with a sensitive thermometer.
	\item Drop the bottle $n$ times (about 20 or 30) in quick succession 
	from the lab bench to the floor.
	\item Immediately measure the final temperature of your lead shot (the rise 
	won't be much).  Record the highest reading the thermometer reaches.
	\item Calculate the mechanical work done from $W=n\,Fd$ where $F$ is the 
	weight (in newtons) of the shot and $d$ is the distance (in meters) from the floor 
	to the lab bench.  The result will be in units of Nm (=joule).  Now convert from joules to calories.
	\item Make a plot of change in internal energy (assumed to be equal 
	to the work done) (in calories) vs. mass times the 
	change in temperature (in g~\degree C).  Your lead shot sample will 
	provide one data point; also acquire the data from the other groups 
	in the class on this procedure for other data points to plot.  It is 
	important to realize that specific heat varies with temperature so 
	this graph won't be a perfectly straight line.  But over small 
	temperature ranges $c$ doesn't change much and so the graph will be 
	approximately linear. 
	\item The slope of your straight line is your experimental value for 
	the specific heat of lead (in cal/g~\degree C) near room temperature; 
	compare it to the accepted value.
\end{enumerate}

\underline{Using equation \ref{compare}}:
\vspace{-.2in}
\begin{enumerate}
	\item Measure the mass of a solid piece of lead or a quantity (1/4 
	bottle) of lead shot.
	\item Suspend the solid lead by a string or the shot in a cup in the steam 
	generator to raise its temperature to the temperature of boiling water 
	(not necessarily 100 \degree C at our altitude).
	\item Put a quantity (about 1/2 the mass of your lead sample) of 
	cold water in the calorimeter and measure its mass and initial temperature.  
	Include 12.2 grams to account for the effect of the aluminum calorimeter cup.
	\item Record the initial hot temperature of the lead.
	\item Quickly dry the lead (if you used the solid) and put it in the 
	cold water in the calorimeter.
	\item As they equilibrate (gently use your stirring rod 
	occasionally), record the highest water temperature as 
	the final temperature for both the lead and the water.
	\item Use these data along with the specific heat for lead (use the 
	accepted value) to compute the specific heat for water (in cal/g~\degree C) from equation 
	\ref{compare}.
\end{enumerate}

Now that you have found the specific heat for water, use the 
procedure above (for equation \ref{compare}) to find the specific 
heat of a different solid metal sample, such as aluminum or steel or 
brass.

\underline{Using equation \ref{latent}}:
\vspace{-.2in}
\begin{enumerate}
	\item Fill your calorimeter cup one-half to two-thirds full of warm 
	water and determine the mass of the water.   Add 12.2 g for the cup.
	\item Record the initial temperature of the water.  Obtain a few ice 
	cubes from a water-and-ice mixture (this ensures that they are very 
	close to 0\degree C) and carefully dry them with paper towels.   Then 
	put them in the calorimeter, being careful not to splash water out, and gently stir until 
	completely melted.  You would like to end as much below room 
	temperature as you started above.  Record the final temperature as the lowest 
	reading after the ice is completely melted.
	\item The mass of the ice is most easily determined by re-weighing 
	the cup now and subtracting the mass of the cup (the true mass, not 
	the 12.2 g) and the original 
	warm water.
	\item Use equation \ref{latent} to compute the latent heat of ice.  
\end{enumerate}

\underline{Apparatus:} As always, sketch the apparatus. 

\underline{Discussion:} 
\vspace{-.2in}

\begin{enumerate}
	\item Why might the results in the first procedure not 
	be very accurate?  (Does \emph{all} of the work change the internal 
	energy of the \emph{lead}?)
% 	\vspace{.8in}
	\item How could one improve the results of this whole experiment?
% 	\vspace{.8in}
	\item Water is often used as a heat storage medium.  Is there a 
	physics reason for this, or is it just cheap and plentiful?  What 
	property of water determines the answer to this question?  How unique 
	is water with respect to this property when compared to nearly all 
	other liquids and solids?
% 	\vspace{.8in}
	\item If you dropped a block of aluminum from the top of a building, 
	would its temperature rise more or less than if you dropped a block 
	of lead?  Explain your reasoning.
% 	\vspace{.8in}
	\item How many calories would it take to raise 100 g of ice at 
	-5\degree C to +5\degree C?  Show your work.  There will be a term 
	in your answer that wasn't in equation \ref{latent} because in the 
	procedure you were careful to start with ice at 0\degree C.  For that 
	term you will need to look up $c_{\rm ice}$.
% 	\vspace{.8in}
\end{enumerate}

\underline{Conclusions:} 

\newpage
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