## Sunday, October 02, 2011

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

There was some strange science going on during the "Stiff" episode of CSI: Miami on 2 October 2011.

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 ]

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.