### Floating hat on "Stiff" episode of CSI: Miami

At the beginning of the show, one gets to see a floating hat. The proferred explanation was that a heavy gas (here propane) hugged the floor, causing the hat to levitate.

The assault weapon turned out to be a snow globe filled with glycerin and white polymer [PE] "snow." But death was caused by the propane. As it happened, the propane did not include a sulfur compound so that leaks could be smelled. [Are people selling unscented propane on the black market?]

See Episode Guide > Season 10, Episode 2

The episode ends with Walter Simmons (played by Omar Miller) playing a joke on Ryan (related to the floating hat).

***As to the science, contemplate the following "worked out" balloon problem from the internet.

The question:

A balloon weighing 80 kg has a capacity of 1200 m3. If it is filled with helium, how great a payload can it support? The density of helium is 0.18 kg/ m3 and the density of air is 1.30 kg/ m3. Express your answer in newtons.

[Observation: Helium has an atomic weight of 4; the effective molecular weight being taken for air is 4 X 1.30/0.18 = 28.9. The molecular weight for propane is 44.1, so the density of propane gas, based on this example, is 44.1/28.9 X 1.30 = 1.98 ]

The answer

Steps to complete the balloon problem:

List all of the variables given.

Mass of balloon = 80 kg

Volume of balloon = 1200 m3

Density of Helium = .18 kg/m3

Density of Air = 1.3 kg/m3

Determine the the total mass that can be lifted by the helium balloon.

Mass lifted = mass of the volume of fluid displaced

Mass = (1200 m3)( 1.3 kg/m3)

Mass = 1560 kg

The total amount that can be lifted = 1560 kg (including balloon, helium and payload)

Determine the mass that is displaced.

Determine the mass of helium.

(1200 m3)*(.18 kg/m3) = 216 kg

Subtract the mass of the balloon and mass of the 1200 m3 volume of helium from the total mass that can be lifted.

1560 kg - 80 kg - 216 kg = 1264 kg

Determine the Force required to lift the displace volume of 1200 m3.

F = mg (where g is gravity)

F = (1264 kg) * (9.8 m/s2)

F = 12,387 Newtons

***

**As to the CSI: Miami hat problem**

If one had a hat of volume 10 liters (=0.01 m3), the mass of propane that would be displaced is

0.010 m3 X 1.98 kg/m3 = 0.0198 kg 0r 0.044 pounds Or 0.69 ounces.

It is unlikely that the hat depicted on CSI: Miami had a volume as high as 10 liters or a mass as low as 0.02 kg.

**That dog won't hunt, and that hat won't float.**

Suppose we jacked the gas up to sulfur hexafluoride, discussed by Walter (Omar). The molecular weight is

146.1 so the density goes up by (146.1/44.1) to 6.56. Then, the mass of SF6 displaced by 10 liters is 0.0656 kg

or 2.3 ounces.

**In passing, similar calculations can be done as to gas vesicles (gvp) in cyanobacteria.

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