# 08 Temperature and Ideal Gases

## Pressure and Projectile – Penguin’s Poop

An interesting paper on the range of penguin’s poop. Their motivation? “Such information is useful for keepers to avoid the direct hitting of faeceses.”

## 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 $$\Delta U=Q+W$$

## 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.

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

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.

This classic physics demonstration is used to show the effects of pressure difference between the atmosphere and a cooling volume of air. With a set of clean apparatus, you can even have the egg for a snack after that.

Materials

1. Hard-boiled Egg
2. Flask or glass bottle with mouth smaller than the egg
3. Paper measuring about 2 cm by 5 cm
4. Lighter

Procedure

1. Peel the hard-boiled egg.
2. Light the piece of paper and drop it into the flask.
3. Place the peeled egg on the mouth of the flask such that the egg seals the flask.
4. Observe the egg being sucked in while the flame dies.

Explanation

When the burning paper enters the flask, it causes the air within the flask to heat up and expand, with some escaping from the flask. When the egg seals the flask, the flame dies as the paper is about to be burned up while oxygen is also running out.

The air then cools down and the pressure within the flask drops. The pressure due to the atmosphere acting downward on the egg is then greater than that acting upward due to the pressure of the cooling air. This pushes the egg into the bottle.