Idealized Stirling Cycle

I created a new GeoGebra app based on an ideal Stirling Cycle (A. Romanelli Alternative thermodynamic cycle for the Stirling machine, American Journal of Physics 85, 926 (2017)) which includes two isothermal and two isochoric processes. The Stirling engine is a very good example to apply the First Law of Thermodynamics to, as the amount of gas is fixed so the macro-variables are only pressure, temperature and volume. Simplifying the cycle makes it even easier for first time learners to understand how the engine works.

For those who prefer to be impressed by an actual working model, it can be bought for less than S$30 on Lazada. All you need for it to run is a little hot water or some ice. Here's a video of the one I bought:

The parts of the Stirling engine are labelled here:
How a Stirling Engine works

My simulation may not look identical to the engine shown but it does have the same power piston (to do work on the flywheel) and displacer piston (to shunt the air to and fro for more efficient heat exchange).

Geogebra link: https://www.geogebra.org/m/pbnw2yas

PV Diagram for an Ideal Gas

GeoGebra link: https://www.geogebra.org/m/xyqhfvyw

Applying the 1st Law of Thermodynamics to 4 simple changes on an ideal gas, students can check their understanding using this Geogebra app. When is work done positive? Which processes bring about an increase in internal energy or temperature? Which processes require heat input?

Stirling Engine

I bought a simple beta Stirling engine online at dx.com recently and it came in the mail today. It works well with a cup of hot water placed under it, although it might take a little push to get it started due to the initial static friction. However, once it starts spinning, the wheel goes on and on for a very long time.

From the video, you can observe the expansion of the air within the main piston cylinder as the heat below raises the temperature and pressure. This forms the power stroke. When the piston rises, it pushes air into a secondary piston, which also helps to provide torque to the wheel. When the air in both pistons expand, it cools down. An understanding of the 1st law of Thermodynamics (JC syllabus) is necessary to appreciate why that happens. Upon cooling, pressure decreases and the pistons fall. The cycle repeats itself.

 

Which Equations Apply Only to Ideal Gases?

Students are sometimes unclear about which of the equations taught in the topic of Thermal Physics apply to ideal gases and which apply to all systems (whether ideal or real gas, even liquids and solid). The following table should help to clarify:

 

Applies to Ideal Gas only Applies to all systems
Gas Laws pV=nRT pV\approx nRT only for gases at low pressure and high temperatures
Average Kinetic Energy =\dfrac{3}{2}kT" /> \propto T" />
Internal Energy U = sum of KE of molecules
U=\dfrac{3}{2}NkT=\dfrac{3}{2}nRT=\dfrac{3}{2}pV
U = sum of KE and PE of molecules
First Law of Thermodynamics applies to all systems \Delta U=Q+W

Adiabatic Process Demonstrations

Here are some interesting lecture demonstrations on adiabatic thermodynamic processes you can carry out. In an adiabatic process, there is no heat transfer between the system and other systems (including its environment.) According to the First Law of Thermodynamics (\Delta U=Q+W), where Q = 0, a compression of a gas which is associated with work being done on the gas will cause the internal energy and hence, the temperature of the gas to rise. On the other hand, when an expansion of a gas takes place, the gas will cool down.

1. Adiabatic compression using a fire syringe

(available from Funlearners for $30 in Singapore)

2. Adiabatic expansion using a fire extinguisher

http://www.youtube.com/watch?v=b6SZI88Odmw

 

 

Boyle's Law

Using a hand-operated vacuum pump, we can demonstrate the relationship between pressure and volume of a gas. According to Boyle's law, the pressure of a gas of constant mass and temperature will be inversely proportional to its volume.

In our demonstration, we will reduce the ambient pressure within the sealed container, hence allowing the higher internal pressure of a balloon to cause it to expand. When the volume within the balloon increases, the internal pressure can be observed to decrease until it is in equilibrium with the surrounding pressure.

While the relationship between pressure and volume is not exactly obeying Boyle's law due to additional factors such as the tension due to the elastic property of the balloon, it does demonstrate an inverse relationship.

Boiling under Reduced Pressure

With the help of a simple manual vacuum pump that is used to keep food fresh, we can demonstrate the effect of a reduced pressure on the boiling point of water. This leads students to a discussion on what it takes to boil a liquid and a deeper understanding of the kinetic model of matter.

Materials

  1. Vacuum food storage jar with hand-held vacuum pump
  2. Hot water

Procedure

  1. Boil some water and pour them into the jar such that it is half filled. This is necessary as hand-held vacuum pumps are not able to lower pressure enough for boiling point to drop to room temperature.
  2. Cover the jar with the lid and draw out some air with the vacuum pump.

Explanation

When water boils, latent heat is needed to overcome the intermolecular forces of attraction as well as to overcome atmospheric pressure. Atmospheric air molecules would prevent a significant portion of the energetic water molecules from escaping as they will collide with one another, and cause them to return beneath the liquid surface.

Removal of part of the air molecules within the jar lowers the boiling point of water because less energy is needed for molecules to escape the liquid surface.

Egg out of Flask

In a previous demonstration, we put a boiled egg into a flask with a mouth narrower than the egg. The challenge is now to remove the egg from the flask without breaking it.

Materials

  1. Flask
  2. Egg
  3. Water
  4. Bunsen burner or candle

Procedure

  1. Pour some water into the conical flask.
  2. Invert the flask quickly over a tray such that the egg seals the mouth of the flask, preventing the water from coming out.
  3. Light a flame and place the part of the flask with water over the flame. This will help prevent the heat from cracking the flask.
  4. Place a tray under the mouth of the flask as the egg slides out to prevent a mess.

Explanation

The flame heats up the air and the water in the flask. The heated air expands while some of the water vapourizes. With the increase in amount of gas and temperature, the pressure within the flask increases.