Balls and Plate, 4A30.22

Topic and Concept:

• Thermal Properties of Matter, 4A30. Solid Expansion

Location:

• Cabinet: Thermodynamics (TD)

• Bay: (A3)?

• Shelf: #1?

Abstract:

A plate with a hole is heated with a set of two balls, one over and one under size. Heat the plate and slip over both.

Important Setup Notes:

• This demonstration requires a supply of methane gas usually provided by the red and white gas carts found in rooms 2103, 2241, (and 2223 upon request).

• This demonstration requires a supply of liquid nitrogen. The main supply is located at the loading dock. If 12 hours notice given to lecture demo, supply will be provided.

Setup and Procedure:

1. To light the burner, connect the attached gas hose to the gas out (red panel) on the red and white gas cart.

2. Open the gas valve.
3. Light a match and bring it near the top of the burner.
4. The flame will ignite the gas. Adjust the flame height accordingly by adjusting the valve.

Option A. Shrinking and expanding the balls

1. Show that the smaller ball can get through the hole and the larger ball cannot.
2. Heat the smaller ball with the burner and show that the smaller ball can no longer fit through the hole.
3. Soak the larger ball in the liquid nitrogen and show that the larger ball can now fit through the hole.

Option B. Expanding the hole

1. Demonstrate to students that the smaller ball can get through the hole and the larger ball cannot.
2. Place the burner beneath the plate to heat it.
3. Show that both balls now fit through the hole.

Cautions, Warnings, or Safety Concerns:

• Always use the gloves and safety glasses throughout this demonstration.
• Beware of the heated plate - contact with skin could cause severe burns!
• Use care when working with the liquid nitrogen - prolonged contact with skin causes severe frostbite!

Discussion:

When the plate is heated, the dimensions of the plate increase while maintaining their relative proportions. In other words, the overall area of the plate expands along with the size of the hole while the ratio of hole area to plate area remains the same. Heating causes the molecular bonds to lengthen, which causes the material to expand. You can think about it this way: a group of people standing in a tight circle with elbows linked try to lengthen their "bonds" by moving to hold hands at arms length. They have to expand the circle by standing back everyone stands further apart. This is analogous to the molecular bonds around the hole. This is considered a 2D expansion (the plate thickness is quite thin relative to the other dimensions) and can be described by

ΔA/A = α_A*ΔT = α_L²*ΔT

where A is the area at temperature T_i, ΔA is the change in area when the material is at temperature T_f, ΔT is T_f - T_i, and α is the coefficient of thermal expansion which depends on the material. The expansion of the balls is also 2D since the quantity of importance is the cross sectional area. See references below for more information.

Videos:

• Lecture Demonstration's Youtube Channel

References:

• Wikipedia - Thermal Expansion

• Wikipedia - Coefficient of Thermal Expansion

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