• The program q a areas units volumes misc might be useful for understanding areas and volumes as well as density.  The complete path is as indicated below:

  http://www.vhcc.edu/dsmith/GenInfo/qa_query_etc/q_a_areas_units_volumes_misc_070104.exe

You observed a system consisting of a soft drink bottle, filled to a depth of about 5 or 6 cm with water.  The system was cooled to a known temperature (the 'outside' temperature, which could be the temperature of a refrigerator or freezer), then capped at that temperature with a cap through which a tube of inner diameter 1/8 inch has been inserted.  The hole through which the tube is inserted is small enough that it is sealed by the tube, and the tube extends down into the water at the bottom of the container so when the cap is tightened no air can enter or leave the system.  When the system is then brought into a room at room temperature, the air in the bottle warms up, first increasing the pressure of the system then, when water begins exiting the tube, expanding.  This requires the addition of thermal energy to the system.  Water exits the system at a certain height relative to the water in the bottle, resulting in an altitude change in that water and a corresponding change in the potential energy of the system.

The system was observed for a variety of altitude changes, in the context of the question of efficiency vs. altitude change.  Another question relates to the effect on efficiency of various 'outside' and 'inside' temperature.

For the system you observed:

• What was the change in the PE of the system?

   

• Sketch a P vs. V graph for each system observed, assuming the volume of the tube to be negligible.  You can sketch more than one graph on a single set of coordinate axes, but you probably can't get them all onto the same set of axes and still see which is which.

   

• Assuming molar specific heat 5/2 R during the part of the cycle where pressure increases, how much thermal energy was introduced into the system during this phase?

   

• Assuming molar specific heat 7/2 R during constant-pressure expansion if this is applicable, or in the case of a quick expansion assuming that no thermal energy was provided, determine the thermal energy introduced into the system during its expansion.

   

• Calculate the 'practical efficiency' of the system, defined as PE change / thermal energy added to system.

   

• How does this compare to the theoretical maximum efficiency of an engine (i.e., an ideal Carnot engine) operating between the two temperatures used in this experiment?

   

• Correct your P vs. V graph for the fact that the volume of the tube is non-negligible.  The cross-sectional diameter of the inside of the tube is 1/8 inch, or about .314 cm.

   

• How would the fact that water is moving through the tube affect the actual practical efficiency of this system?  How could you use the results of previous experiments to estimate the magnitude of this effect?

   

• How would tube length affect the practical efficiency of the system?  Again quantify as best you can.