Heat engines

Objectives

In this lab students will experiment 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.  Students will verify experimentally that the useful mechanical work done in lifting a mass m through a vertical distance y is equal to the net thermodynamic work done during a cycle as determined by finding the enclosed area on a P-V diagram.  Students will compare the mechanical work mgy with the net work done by the engine in an engine cycle, which is given as a function of pressure and volume changes by the expression.

Wnet=∮PdV

Students will use he PASCO TD-8572 Heat Engine/Gas Law Apparatus for their investigations of a working heat engine.  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 or to a pressure sensor with tubing.

The apparatus includes the following equipment:

* Base apparatus 
　Piston diameter: 32.5 mm ± 0.1mm
　Mass of piston and platform: 35.0 g ± 0.06g
* Air chamber
* 3 hose configurations:  one with one-way check valves, one with a clamp, one plain piece of tubing
* 1 one-holed and 1 two-holed rubber stopper
 

Part A

Procedure:

In part A you will familiarize yourself with the equipment.

The heat engine is placed on a table.  A rotary motion sensor is mounted on a rod high above the engine.  A string attached to the platform of the engine passes over the pulley of the rotary motion sensor and a 50 g mass hanger is attached to the other side of the string.  As the piston and the platform move up and down the pulley turns and the rotary motion sensor feeds the angle through which it has turned to the computer.  The radius of the pulley is known.  The position of the piston above its starting position is therefore given by position = angle (in radians) times radius.  The computer computes the position of the piston and the volume of the gas in the cylinder of the heat engine (volume = area times height).

The air chamber is connected to the heat engine using the tubing with the one-way valves. 

A Pasco low-pressure sensor is connected to the other port of the heat engine.  The low-pressure sensor measures the pressure in the chamber with respect to some reference pressure and feeds measurement to the computer.

A cup up ice water and a cup of hot water are placed next to the heat engine and the air chamber is placed into the ice water.

A 200g mass is placed onto the platform.

The air chamber is moved from the ice water bath to the hot water bath.  The air in the chamber quickly expands through the tubing and moves the piston up.  The one-way check valve in the tubing connecting the base apparatus and the air chamber permits air to enter the cylinder, while the other one-way check valve prevents air from leaving through the branched tube.  The air chamber is moved back to the cold bath and external air is sucked into the air chamber through the one-way valve located at the end of the branched tube.  The one-way valve in the connecting tube prevents the air from escaping from the piston, so the height of the piston remains the same.  These steps are repeated until the mass has been lifted approximately 8 cm.  Watch the video clip.  Move the cursor over the video clip to start the movie. 

The computer records the pressure (in units of kPa) and the volume of the gas in the cylinder (in units of cm3) as a function of time  and produces the plot of pressure versus volume shown below.

Answer the following questions:

1) What happens to the volume of the gas as the air chamber is moved back and forth between the cold and the hot water cups?
2) What happens to the amount of air in the system?
3) What happens to the density of the air in the system?
4) What happens to the pressure in the cylinder?

Part B

Procedure:
In part B you will determine the work done by the heat engine.
With no mass on the platform, the piston is raised ~4cm, and the air chamber with tubing without one-way valves is connected to the engine.  The piston stays at a height of ~4cm.

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 1:

(a)  The air chamber is placed into the ice water.
(b)  A 100g mass is placed on the platform.
(c)  The air chamber is placed into the hot water.
(d)  When the volume is no longer increasing, the mass is removed from the platform.
(e)  The air chamber is placed back into the ice water.
 
When the piston has returned to the original position data acquisition stops.
The computer has produced the plots shown below:

Plot of piston position versus volume

Plot of piston position versus time

Measurement 2:
The experiment is repeated with but a 200 g mass is placed on the platform.

(a) The air chamber is placed into the ice water.
(b) A 200g mass is placed on the platform.
(c) The air chamber is placed into the hot water.
(d) When the volume is no longer increasing, the mass is removed from the platform.
(e) The air chamber is placed back into the ice water.

When the piston has returned to the original position data acquisition stops.
The computer has produced the plots shown below:

Plot of piston position versus volume

Plot of piston position versus time

Data Analysis:

For the two measurements:

Determine the enclosed area on your P-V diagram.  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)=(1000N/m2)(10-6m3)=10-3Nm=10-3J.

Determine the area in units of J. This area represents the work done by your heat engine.

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.

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.

Answer the following questions:

1) 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?
2) What happens to the pressure and the volume as the air chamber is moved from the cold into the hot water?
3) What happens to the pressure and the volume as the mass is removed from the platform?
4) What happens to the pressure and the volume as the air chamber is moved back into the ice water?
5) How does the thermodynamic work compare to the useful mechanical work?