Tuesday, May 1, 2012

Thermodynamics of Ghost Hunting

For about a decade there has been a TV show about two plumbers who try to “scientifically” detect and communicate with ghosts. There are all kinds of problems with this, but let's just confine ourselves to one aspect that relates to physics. One sign of ghostly activity they look for is a localized “cold spot.” The plumbers frequently explain this as follows: “The theory is that spirits drain heat energy from the environment and use it for manifestations.” (The “manifestations” include the sudden collapse of unstable piles and the sort of faint knocking noises houses make as they cool overnight.) How much energy are we talking about? Let's assume that the cold spot is the exact size and shape that the body of the haunting ghost had in life, which may have had a mass of 75 kg. The density of the human body is close to that of water, so each kilogram of mass corresponds to one liter of volume. The volume of the cold spot is then 75 L, or 75000 cm^3.

In a typical investigation, the ambient indoor temperature might be 65 degrees (291.483 K), and the cold spot might be as low as 60 degrees (288.706 K). The temperature drop in this case is 5 degrees or 2.777 K. According to Wikipedia, the volumetric heat capacity of air under typical room conditions is 0.000121 J / (cm^3 K). This means the total energy extracted from the cold spot is 25.2 J, enough energy to lift a 1 kg (2.2 lb) mass 2.57 m (8' 5”). The plumbers have never seen anything like this.

A major problem with their “theory” is that a ghost would be constrained by the First Law of Thermodynamics (conservation of energy) but not by the Second Law of Thermodynamics (which implies you cannot just convert ambient heat energy into useful energy the way they imply). Maybe, though, the ghost is making use of a temperature difference – say, the temperature difference between the room and its grave, which we take to be 48.5 degrees (282.317 K, the average temperature of Akron Caves in NY). If there were some way to make a thermal connection between the two, the flow of heat could be used to do useful work; that is how steam engines and internal combustion engines work. The maximum efficiency of a cyclic engine (the cycle means it can keep going) is given by the Stirling efficiency: Efficiency = (TH – TC) / TH, where TH is the absolute temperature of the heat source (the room, at 291.483 K) and TC is absolute temperature of the heat sink (the grave, at 282.317 K). The efficiency in this case is thus 3.14%. The total amount of useable energy, then, for a Stirling engine operating between the temperature of the room and the temperature of the grave and reducing the temperature of 75 L of air by 5 degrees is 0.8 J – much smaller than before, but still enough to lift a 100 g (3.5 oz) mass 81 cm (32") or to swing a door with a moment of inertia of 7 kg m^2 at an angular speed of 0.48 rad/s or 28 degrees per second.

That sounds more reasonable. Kinda. The real problem, of course is with the oddball mixture of spirits (which are by definition incorporeal) and physics (which only applies to the corporeal).

Oh, and the "practical upshot" would seem to be: If you are annoyed by a haunting, turn down the thermostat. If the ghost is using the Stirling Engine approach above, it would not be able to extract any useful energy if the temperature of your house is the same as the temperature of its grave.

What are we to make, then, of those ghost sightings in winter, frequently outside, where the temperature is less than that of the grave?

1 comment:

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