Re: How do I find information on contraction & expansion by heat or hot water?

Hi Brian,

Ping Pong balls are made of very thin and resilient plastic.

Many hollow plastic objects are made by using molds of two halves of the final object. The liquid plastic is poured into the mold and solidfies almost instantly. Sometimes the plastic is pressed between an inside and an outside mold to ensure a more uniform thickness or to speed production. For an all plastic construction, the two parts are joined together with more plastic (almost like a weld).

Ping Pong balls are made the same way but with more care to ensure the right thickness.

Ping Pong balls are pretty much air tight (until they crack). So the same amount of air is instead all the time. Two things to consider for the ping poing ball.

1) The equation of state of the air inside the ball. Like most analysis of pressure and volume we can start from the Ideal Gas Law. It will not be perfect, but it is easy and gives the right trends.

PV = nRT

where P = pressure
      V = volume
      n = amount of molecules (usually expressed in moles)
      R = Ideal Gas Constant
      T = temperature (usually in Kelvin)

2) An understanding of the properties the ball (shell). The elastic limit is the amount of distortion an object/material can experience and still return to its original form.

When the ping pong ball bounces or is gently pushed on it will distort slightly and the restoring forces of the plastic surface will return the ball to its original shape. The pressure and volume will only change slightly and temporarily in this case, and the dominant term in the shape of the ball is the plasticity of the ball.

However, if you squish a ping pong ball without cracking it, the ball goes beyond its elastic limit. To restore the ball to its original shape work must be done on the ball because it cannot restore itself. A good candidate for restoring the ball is the air inside the ball, since the ball has to be pushed out to its original form and PV is in the same units as work/energy. Pressure is force/area. So a significant internal pressure must be established to push the ball back into shape and reverse the deformation. Sometimes the deformation is irreversible (i.e. cannot be undone).

By raising the temperature of the ball and the air inside the ball, the product PV must go up. The temperature going up is a measure of heat/work being added to the ball/water system. As the temperature goes up, at first the volume of the squished ball will not change -- therefore the pressure of the air will rise and the volume of the air will stay the same. Once the pressure gets to a critical value, the ball will start to reshape. The reshape will slightly reduce the pressure as the volume available for the air goes up. If the water is hot enough, the air will be able to perform enough work on the shell to return it to original form. I suppose that the hot water will make the plastic a little more pliable and will more easily move, as well.

If the water gets too hot, either the shell will become too soft and irreversibly deform or will crack if the pressure inside gets to high. I suspect getting the pressure inside to get too high and cause the ball to rupture would very difficult to do at home or at school because this will take a lot of heat. Please be careful when working with pressure and heating. It is very easy for something to break and cause injury.

Sincerely,

Tom "Boiling Point" Cull