Temperature of Neon Light

Question

I recently installed a neon light in a configuration such that it is resting on a book shelf and near some books. I would like to know if this stupid/if it is going to start a fire if I leave it on without watching it. I'm also curious about how to calculate the temperature of the bulb by physical principles.

To be clear, I'm not going to leave the bulb on when I am not present and/or not awake until I've measured the equilibrium temperature and it is sufficiently low.

Parameters: the bulb is a 5 feet long. The outer radius is approximately 1.5cm. I don't know how thick the glass is. The bulb contains argon and mercury and emits a pink color. It presumably is made of glass and has a coating. By touch, the cathode/anode (? -- I think this is the terminology) is the hottest part. These nodes are enclosed in a plastic insulator. I can touch the lamp and the ends without burning myself after a few hours of it being on, which I am taking (correctly?) to be the equilibrium temperature. The lamp is at STP, defined as: in a room at atmospheric pressure and temperature, out of direct sunlight, and with ambient temperature unlikely to exceed 110 degrees F/45 degrees C at any time. (yes, I am American).

I can make more measurements or determine them with some amount of money/materials/effort if I have a sense of what the important measurements are.

So: the questions are:

(1) Practical: Should I worry about starting a fire

(2) Theoretical: How do I calculate the equilibrium temperature of the bulb given the voltage, current, number density of the gas, ratio of the two species, absorptive properties of the coating, length and inner+outer radius of the cylindrical glass bulb, and pressure and temperature of the surroundings. Or any other parameters I might not be thinking of.

(3) Characteristic: What are the characteristic values of these parameters that I should use.

Progress so far: the Internet tells me that Neon lights are a plasma with electron temperature between $10^5$K and $10^6$K, and plasma density between $10^{12}$ and $10^{20}$ in units of $cm^{-3}$. I don't know what this means. I would appreciate a reference.

Answer 1

here is a simplified way to estimate whether or not you are in trouble.

on the box which encloses the high-voltage power supply for the neon tube, there will be a power rating for the box which will say something like "120VAC 1.5A input" possibly accompanied by something else which reads like "5000VDC 30ma output MAX". these numbers refer to the input power consumed by the power supply from the AC mains (120VAC x 1.5A = 180 watts) and the maximum amount of power it can deliver to the neon tube (5000VDC x 0.030A = 150 watts, slightly less than the input power due to losses in the power supply).

Assume now that the neon tube is drawing the full rated output power, 150 watts in this example, to power up the tube, whose surface area you can calculate knowing its length and diameter. Assume further that all that electrical power is dissipated as heat in the tube (a worst-case assumption). Now you can calculate the worst-case power density in watts per square centimeter which the tube will produce as it sits upon your shelf.

Finally, we assume that half the tube output will be radiated away from the shelf into the room and half will be absorbed by the shelf. This represents the heat load which the shelf must dissipate else it will ignite. Now you must answer the final question: If the shelf, which we assume is wood, is presented with a heat input of x watts/square centimeter, will it begin to burn?

I can tell you now that the answer will be No, based on experience, and that the tube and shelf will be safe: because the wattage produced will be insufficient to raise the temperature of the wood to the ignition point.