# Incandescent tungsten **URL:** \ **Category:** Factual Questions\ **Created:** [November 27, 2015, 2:20pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705 "2015-11-27T14:20:55Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 27, 2015, 2:20pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/1 "2015-11-27T14:20:55Z")
Inspired by a combination of two XKCD What-Ifs: [Hair Dryer](http://what-if.xkcd.com/35/), which postulates the effects of a one-meter cube radiating heat at certain power levels; and [Extreme Boating](http://what-if.xkcd.com/50/), which mentions a lake of liquid tungsten. It occurred to me that in the lake of tungsten example the writer declined to note just how much radiant heat and light the surface of the lake would be giving off. If you think an unfrosted incandescent light bulb is uncomfortable to look at, consider that that’s what a tiny filament of hot tungsten is doing. Even if the boat were magically heat-proof and insulating and this was taking place in a vacuum, just the radiant energy would fry you like the flash of a nuclear explosion. So going back to the one-meter cube example, if it were made of tungsten just under it’s melting point (I’ll ignore oxidation from the surrounding air for this example). can someone with a better grasp of thermodynamics tell me just how much heat and light it would be emitting? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 27, 2015, 2:57pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/2 "2015-11-27T14:57:01Z")
This actually isn’t too hard. The melting point of tungsten is 3695 K. The total power radiated is given by P = σT[sup]4[/sup], where [σ = 5.670367×10[sup]−8[/sup] W m[sup]−2[/sup] K[sup]−4[/sup]](https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_constant) . Just plug in the temperature of the cube and its area (6 m[sup]2[/sup]), and we get that the power is about 63 megawatts. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 27, 2015, 3:33pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/3 "2015-11-27T15:33:54Z")
Which translates into what in terms of light and heat? I.E., at what distance would the illumination be as bright as sunlight? What distance to broil a steak? ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [November 27, 2015, 3:45pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/4 "2015-11-27T15:45:44Z")
Referring back to the hair dry xkcd, 63 megawatts is about halfway (log-scale) between his 18 MW & 187MW settings. His lesser scenario is a 2400C box glowing bright yellow. The greater is white hot. 63MW is also on the order of a million household lightbulbs, or a hundred thousand household ovens. So we’re talking serious energy flux. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 27, 2015, 4:15pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/5 "2015-11-27T16:15:13Z")
> [@Lumpy](#): > > Which translates into what in terms of light and heat? I.E., at what distance would the illumination be as bright as sunlight? What distance to broil a steak? At 3695K, the flux at the surface is about 1/6 that of the Sun. So if you stand at a point where the apparent size (area) of the cube is 6 times that of the Sun, you’ll receive the same amount of radiative heat. So, about 57 meters. I don’t know what temperature is necessary to broil a steak, but I think broilers usually get up to about 400 F (480K)? An object at 480K radiates (480/3695)^4=1/3500 as much as at 3695, so at a distance where the cube fills 1/3500 of your view, the equilibrium temperature will be 480K. That’s about 5 meters. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [November 27, 2015, 9:43pm UTC](https://boards.straightdope.com/t/incandescent-tungsten/738705/6 "2015-11-27T21:43:52Z")
> [@scr4](#): > > At 3695K, the flux at the surface is about 1/6 that of the Sun. So if you stand at a point where the apparent size (area) of the cube is 6 times that of the Sun, you’ll receive the same amount of radiative heat. So, about 57 meters. > > I don’t know what temperature is necessary to broil a steak, but I think broilers usually get up to about 400 F (480K)? An object at 480K radiates (480/3695)^4=1/3500 as much as at 3695, so at a distance where the cube fills 1/3500 of your view, the equilibrium temperature will be 480K. That’s about 5 meters. The math is beyond me but five meters sounds way too low.