How can we do work with heat? How can we convert some disordered energy back into ordered energy?
In this exercise you will analyze data obtained with is a “real” thermal
engine that can be taken through a four-stage expansion and compression cycle
and that can do useful mechanical work by lifting small masses from one height
to another. You will determine the useful mechanical work
done by the engine by
measuring the vertical distance y a mass m is lifted. You will compare
this mechanical work Wmech = mgy to the net
thermodynamic work done during a cycle. The pressure as
a function of volume is recorded for one cycle, and the net thermodynamic
work done by the engine equals the enclosed area on
the PV diagram,
Wnet = ∫closed path PdV.
The PASCO TD-8572 Heat Engine/Gas Law Apparatus is used to obtain the data. The heart of this apparatus is a nearly friction-free piston-cylinder system. The graphite piston fits snugly into a precision-ground Pyrex cylinder so that the system produces almost friction-free motion and negligible leakage. The Heat Engine/Gas Law Apparatus is designed with two pressure ports with quick-connect fittings for connecting to an air chamber and a pressure sensor with tubing.
With no mass on the platform, the piston is raised ~4 cm, and the air chamber with tubing is connected to the engine. The piston stays at a height of ~4 cm.
The computer is set up to record the pressure (in units of kPa), the volume of the gas in the cylinder (in units of cm3), and the position of the cylinder above its starting position (in units of m) as a function of time and to produce plots of pressure versus volume and position versus time.
|Data acquisition starts.
Click on the thumbnails to see a larger picture.
(a) The air chamber is placed into ice water.
|When the piston has returned to the original position data acquisition stops.|
|The computer has produced the plots shown below
Plot of pressure versus volume:
Plot of piston position versus time:
|Determine the enclosed area on your P-V diagram. (Estimate the area of
the parallelogram by multiplying its width by its height.) The y-axis has
units of kPa and the x-axis has units of cm3. The area therefore
has units of (kPa)(cm3). (1 kPa)(cm3) = (1000 N/m2)(10-6
m3) = 10-3 Nm = 10-3 J.|
Determine the area in units of J. This area represents the work done by your heat engine. Record it in a table.
|From the position versus time graph determine the distance y the mass has been lifted, i.e. the difference in the positions of the platform just before the mass was put on and just before it was taken off the platform. (The y-axis in this graph has units of m.)|
|Find the change in potential energy mgy of the mass (in units of J), which is equal to the mechanical work done on the mass. Record it in a table.|
|Calculate the %difference between the two values.|
||Work done by heat engine
from P-V diagram (J)
|Change in potential
energy of mass (J)
Paste your table into your Word document and answer the following questions..
|The engine starts with an empty platform and the air chamber in ice water. What happens to the pressure and the volume when the mass is placed on the platform?|
|What happens to the pressure and the volume as the air chamber is moved from the cold into the hot water?|
|What happens to the pressure and the volume as the mass is removed from the platform?|
|What happens to the pressure and the volume as the air chamber is moved back into the ice water?|
|How does the thermodynamic work compare to the useful mechanical work? What about conservation of energy?|
Save your Word document (your name_exm3.docx), go to Blackboard, Assignments, Extra Credit 3, and attach your document.