## II. Procedure

1.      Weigh your sample of Pb shot.  (You should use no less than 50 grams.)  Measure room temperature.

2.      Place the outer can of the calorimeter with its insulating (large) Styrofoam cup and insulating ring on the balance.  Put the Pb sample in a small Styrofoam cup and place it on the pan next to the calorimeter. The total mass of the system will eventually include the mass of a Styrofoam cup with liquid nitrogen, but you may want to balance the scales now.

3.      With the timer, and with pencil and paper at hand, be ready to record the mass on the balance as a function of time.  You will later want to plot mass on the balance versus time.  Your mass will decrease by around 50 grams during the experiment.   Thus your mass axis should be expanded to include only this 50 grams, from the total starting mass of your whole system to the total finishing mass.

4.      Obtain a sample of liquid nitrogen in your small Styrofoam cup and place the Styrofoam cup into the ring on the calorimeter.  Rebalance the scale.  Your weights should contain several 10 g and 20 g masses that can be removed as the nitrogen evaporates.  After you have achieved a balance, move the sliding mass down to the next lowest even integer mass (i.e., 0,2,4,6,8).  This will unbalance the scale.  As the nitrogen evaporates, the pointer will swing back through the balance point.  At this time, start the clock.  The clock will continue to run for the remainder of the experiment.  The total mass on the balance at this time is your t = 0 mass and should be plotted on your graph as such.

5.      Continue to move the sliding mass down in 2-g steps and record the times when the pointer goes through the balance point.  When the sliding mass gets to 0 you will need to remove 10 g from the pan and move the slidewire mass to the 8-g mark.

6.      When you have 6 or 7 points, it should be obvious from your data that your plot will be a straight line.  The slope of this data gives you a background loss rate.  At this point, transfer your Pb sample into the liquid nitrogen as quickly as possible (the clock is still running) but without splashing any nitrogen or putting your fingers in it.  Be sure to note the time when you add the Pb and remember to put the empty glass beaker back on the balance pan.  The nitrogen will boil rapidly and you should try to take data again as soon as you can, i.e., mass versus time.  You will need to remove mass (more than two grams) from the pan to regain your equilibrium.  Be sure to record the amount of mass removed at this time!

7.      Continue taking data until you again have 6 to 8 points.  The slope of this data is your new background loss rate.

8.      Call up Excel and enter your data. The plot want will be one of mass versus elapsed time. However, we want two separate data series on the same graph, one for each background rate, so that we can get two separate best-fit lines. Enter your data from before you added the Pb as one series and enter the data from after you added the Pb as the other series. Now obtain two least squares fits to the two background loss rates; i.e., fit the first set of points separately to a straight line and then fit the second set of points to a straight line.  You can extend these lines by right-clicking on the line and selecting format trendline.  Then under options, select forecast forward/backward about 100 units.  Get a printout of the graph and the spreadsheet.

9.    Using the graph that you have just printed out, you will now determine the amount of liquid Nitrogen that was lost when you added the Pb. You want the best value for the mass that you can get.  You can obtain this mass numerically by using the transfer time in the equations for your best-fit lines and then taking the difference between the mass before and the mass after.  Alternatively, you can obtain the change in mass graphically by following the procedure in step 10 below.

10.  Expand the y-axis to be as large as possible. This will mean that some of your data may not show up on this new graph (which is why you printed out the original graph in part 8). Right-click on the y-axis of your graph. Choose format axis. In the Patterns menu click the option for minor tick marks (inside). Then, go to the Scale menu to format the minor tick marks and the scale of your graph. Choose 1 for the size of the minor unit for tick mark. Now format your y-axis so that it just includes the points of interest, namely, the last point few points from before the Pb was added and the first few points after the Pb was added. Get a printout of this graph.  On this new graph, choose a time midway between when you transferred the Pb and when the background rate was re-established. Draw a vertical line at this time. The points at which this vertical line intersects the two background lines define the mass of nitrogen that boiled off to cool the metal. This mass is read off the vertical axis.

11.  Using the specific heat of Pb and its change in temperature, you can find the amount of heat lost by the Pb and hence the heat absorbed by the liquid nitrogen. Using the heat absorbed by the liquid nitrogen and the mass of the nitrogen boiled off by the lead, calculate the latent heat of vaporization of nitrogen and compare it to the book value of 197.7 J/g. Compare to your measured value by calculating the percent error. How do you account for any discrepancies? Do the problems you've considered make the agreement better or worse?