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Imagine a blast furnace has molten iron of 1,811 K and a gas temperature of 1,173 K. Must the gas have an equal temperature to that of the iron, or is my example accurate that the temperature in gases aren't as hot as those in solids or liquids?

Opening an oven and experiencing a wave of heat against my face, or even having my hand over a candle flame gives me reason to suspect when it comes to conduction, the material is hotter than the air. I gather this is because gases aren't as dense, or perhaps there isn't a closer bond.

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The basics of heat transfer with regards to convection, conduction, and radiation go over this.

The furnace has a heat source which obviously isn't the air itself. There's a coefficient that dictates the temperature difference between the two in the basic equations of heat transfer (it depends on many factors like the speed of convection in the gas and surface area of the element). They show that the gas should be a lower temperature. Depending on the conditions the gas may be a closer temperature or further temperature from the element's temperature.

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The main reason you feel the heat of an oven, or a flame, is not conduction or convection but radiation. Radiation is an electromagnetic wave. The radiation humans "feel as heat" has a slightly longer wavelength than red light, and of course very hot objects such as a candle flame or molten metal also emit visible light as well as heat radiation.

Since electromagnetic radiation passes through air without being absorbed, it does not heat up the air between the hot object and you. The heat energy is absorbed by your body when the radiation reaches it. The air in contact with your body is not being heated as much as your body itself.

In an enclosed space like a furnace, conduction and convection also take place, but most of the heat transferred between the molten metal and the walls of the furnace is by radiation, not conduction and convection from the metal to the gas and then from the gas to the walls.

Radiation occurs at any temperature above absolute zero, but the amount of energy radiated is proportional to the $T^4$ where T is the absolute temperature. So if a piece of material is heated from room temperature (say 300K) to 1800K, the hot material radiates about $(1800/300)^4 = 1296$ times as much heat as when it was cold.

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  • $\begingroup$ He asked about the heat of the gas vs. furnace temperature. As true as this is it doesn't actually answer what he asked. $\endgroup$
    – JMac
    Commented Jan 23, 2017 at 10:53
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in your baking oven the air will be the same temperature as your cake because both are in a closed system. it doesn't matter what is the heat source in a closed system. it will equilibrate almost completely given sufficient time.

if you briefly open and close the oven door, the air inside will be suddenly cooler than the baking cake, but it will warm up again and equilibrate over a minute or so.

if you then put the cake on top of your oven and hold your hand above it you will still feel warm air, but it will be at a lower temperature. in this case, the cake is the heat source, ambient air is only briefly able to exchange heat via conduction before it rises to your hands.

if you put your cake outdoors in the wind, and hold your hand behind the cake, you feel almost no temperature rise, because the air moves so fast past the cake that its temperature does almost not rise.

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