THE INCREDIBLE MASS LIFTER

Written by Naomi Ndavu, during the spring semester 2001 while in Physics II with Dr. Don Collins, at Warren Wilson College

The "Incredible Mass Lifter" is based on the four laws that govern the behavior of gases, i.e. Charles Law, Boyles Law, Guy Lussac’s Law and the Ideal Gas Law. The mechanisms of each of these laws are used in this lab to develop a thermodynamic cycle: a method of obtaining useful work from thermodynamics.

The machine was constructed from a low – friction syringe, a thin connecting tube, an Erlenmeyer flask and two jars of water at different temperatures. Before we started the experiment we made predictions for what we thought would happen, a diagram of the expected results is shown below.

 
Position in cycle Temperature of system Physical changes
A Cold Constant temperature, constant pressure, constant volume
A - B Cold - Cold Constant temperature, increase in pressure, decrease in volume
B Cold Constant temperature, increase in pressure, decrease in voulme
B - C Cold - Hot Constant pressure, increase in temperature, increase in volume
C Hot Constant temperature, constant pressure, constant volume
C - D Hot - Hot Constant temperature, decrease in pressure, increase in volume
D Hot Constant temperature, constant pressure, increase in volume
D - A Hot - Cold Constant pressure, decrease in temperature, decrease in volume

 
The piston of the syringe was held at a constant position (4.4 cc) and the Erlenmeyer flask was closed. The flask was then immersed in a jar of warm water and the piston of the syringe moved up. The increase in volume was noted (9.9 cc). This was done so that we would know just how much of an increase would occur when we eventually removed the load from the piston at the end of the experiment (so as to ensure that no accidents occurred with the glass piston). The flask was then immersed in a jar of cold water (ice and water mixture) the volume at this point was 4.4 cc. Once the piston was stable i.e. it was no longer moving a mass of 50g was placed on it. The piston moved down, and the new volume was noted (0.8 cc). The Erlenmeyer flask was then placed in a jar of warm water and this resulted in the piston moving upwards. The new volume was noted (7.2 cc). The mass was carefully lifted off of the piston and the volume of the syringe increased (9.9 cc).The flask was then returned to the ice and water mixture. The piston moved down and the volume decreased to 4.4 cc. The results we obtained were the same as the predictions we had made earlier. We used this information to construct a “thermodynamic cycle”, shown below.
The area under the graph is equal to the work done by the “Incredible mass lifter”.

WORK= Area of the rhombus
=(1/2 * 3.6 * 2925.69) + (2925.69 * 2.8) + (1/2 * 2.7 * 2925.69)
= 5266.242 + 8191.932 + 3949.682 = 17407.9 N/m2.ml


1000 ml = 0.001 m2
17407.9 N/m2.ml = 0.01741 N/m2 * m3 = 0.01741 J

 
Quantity
Atmospheric pressure
94,628.8 N/m2
Area of piston
1.709 * 10 –4 m2
Mass of piston
0.016 kg
Work (m*g*h) 
19.6 * 10-3 J
Work (area under the parallelogram)
17.41 * 10 –3 J
% Difference
11.2 %

CALCULATIONS:
 

Diameter of piston = 1.475 cm

100 cm = 1 m

1.475 cm = (1.475 cm * 1 m) /* 100 cm = 1.475 * 10–4 m2

Area of piston = pr2 = p (7.375 * 10-3) 2 = 1.709 * 10-4 m2

Atmospheric pressure = 710 mm Hg

1mm Hg = 1.333 * 102 N/m2

710 mm Hg = (710 mm Hg * 1.333 * 102 N/m2) / 1 mm Hg = 94,643 N/m2


Pressure = Force / Area
Pressure of the system at A:

(0.016 kg * 9.8 m/s2) / (1.709 * 10-4 m2) = 917.49 N/m2
917.49 N/m2 + atmospheric pressure = 95560.49 N/m2

Pressure of the system at B:
A mass is added to the system, pressure increases:

(0.016 kg + 0.05 kg) * 9.8 m/s2 / (1.709 * 10-4 m2) = 3,784.67 N/m2
3,784.67 N/m2 + atmospheric pressure = 9,8427.67 N/m2
Pressure of the system at C:
Same as pressure at B

(0.016 kg + 0.05 kg) * 9.8 m/s2 / (1.709 * 10-4 m2) = 3,784.67 N/m2

3,784.67 N/m2 + atmospheric pressure = 9,8427.67 N/m2
Pressure of the system at D:
Same as pressure at A
(0.016 kg + 0.05 kg) * 9.8 m/s2 / (1.709 * 10-4 m2) = 3,784.67 N/m2
3,784.67 N/m2 + atmospheric pressure = 9,8427.67 N/m2

Work done to move the piston = m*g*h

H = D volume / Area

(7.2 * 10-6 m3 – 0.8 * 10-6 m3) / (1.709 * 10-4 m2) = (6.4 * 10-6 m3) 
= (6.4 * 10-6 m3) / (1.709 * 10-4 m2) = 0.0375 m
»0.04 m
WORK = 0.05 kg * 9.8 m/s2 * 0.04 m = 0.0196 J
= 19.6 * 10-3 J
% Difference between work (m*g*h) and work (area of rhombus)
(2.2 * 10-3 J) / (19.6 * 10-3 J) * 100% = 11.2 %
Conclusion: 
The large percentage difference indicates that there were some errors made in the experiment. These errors could have been made when obtaining the different volumes of the syringe, when measuring the diameter of the plunger etc.However, the experiment was a success in that we were able to study and understand the three different gas laws (Guy Lussac’s Charles and Boyle’s) as well as apply the principles of each to the construction of a thermodynamic cycle, which we were able to use for work. 

Links for more information:
 http://www.warren-wilson.edu/~mtanioka/webpage.htm
 http://www.warren-wilson.edu/~cteow/FormalReport2/Charles'Law2.htm