## Extra Credit 3

### A heat engine

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.

Procedure:

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.

Measurement:

• Data acquisition starts.
Click on the thumbnails to see a larger picture. (a) (b) (c) (d) (e)

(a)  The air chamber is placed into ice water.
(b)  A 100 g mass is placed on the platform.  The weight of the mass increases the pressure at constant temperature, and the volume and therefore the height of the piston decrease by some amount.
(c)  The air chamber is placed into hot water.  The temperature rises and the gas expands.  The volume and therefore the height of the piston increase.
(d)  When the volume is no longer increasing, the mass is removed from the platform. Removing the weight decreases the pressure at constant temperature, and the volume and therefore the height of the piston increase by some amount.
(e)  The air chamber is placed back into the ice water.  The temperature decreases and the gas contracts.  The volume and therefore the height of the piston decrease.

• 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:

Data analysis:

• 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.  T
he area therefore has units of (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.
mass

Work done by heat engine
from P-V diagram (J)
Change in potential
energy of mass (J)
% difference

0.1 kg