What exactly are the requirements for a filament?

Not possible, due to the Second Law. If you try it, no matter what the emissivity profile of your objects, the object being heated will end up radiating away energy faster than you can dump it in.

Not entirely. When I go upstairs tonight to take a shower before I go to bed, the first thing I will do is turn on the lights in the bathroom, four 60 watt bulbs. Now why do you suppose I do that? I have a dimmer switch and dim it during the summer. I guess I could summer bulbs and winter bulbs and the latter would be incandescent.

I bet nearly everybody here would, if asked, guess that Edison invented the tungsten filament. The actual inventor was

Joseph Swan.

The Wikipedia article on emissivity is a decent start. It begins with this:

“The emissivity of a material (usually written ε or e) is the relative ability of its surface to emit energy by radiation. It is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature. A true black body would have an ε = 1 while any real object would have ε < 1. Emissivity is a dimensionless quantity.
In general, the duller and blacker a material is, the closer its emissivity is to 1. The more reflective a material is, the lower its emissivity. Highly polished silver has an emissivity of about 0.02.[1]”

Who did invent the Tungsten filament?

Things are never this simple. Here is an excerpt from Wikipedia. I have no idea who really has priority. I would not have guessed Edison, but I might have guessed Langmuir, and I would have been way off.

[Quote=Wikipedia]

Incandescent Bulb

On 13 December 1904, Hungarian Sándor Just and Croatian Franjo Hanaman were granted a Hungarian patent (No. 34541) for a tungsten filament lamp that lasted longer and gave brighter light than the carbon filament. Tungsten filament lamps were first marketed by the Hungarian company Tungsram in 1904. This type is often called Tungsram-bulbs in many European countries.[37] Their experiments also showed that the luminosity of bulbs filled with an inert gas was higher than in vacuum.[38] The tungsten filament outlasted all other types.

In 1906, the General Electric Company patented a method of making filaments from sintered tungsten and in 1911, used ductile tungsten wire for incandescent light bulbs.

[/Quote]

So, back to the OP, why can’t I take tungsten, mix it up with sand, sinter it into a pellet, and use that as filament? The cross-sectional area could be made the same, and this would be easier to make.

Think about your power/surface area.

Also, I’m not sure what you mean but the cross-sectional area being the same. It’s kind of by definition that if the pellet is the same diameter as the filament, then it’s length must be the same.

A coil of tungsten has much more surface area to glow white-hot, and is also much more suited for the conducting of current through it. I’m sure other, more practical applications apply as well in assembling a workable bulb during manufacture and while functioning within a common lamp.

But in general, you want as much exposed surface area as possible to glow. Most of the energy/heat will be wasted from its unexposed insides as infrared if you heat up a lump of tungsten to the same temperature.