# When I'm in a warm room how much of the warmth I feel is due to radiation from surfaces?

Say I'm in a room heated to 23C, once the temperature is in balance all the objects will also be 23C and radiating heat towards me. How much of the warmth I feel is due to this radiation, and how much is due to conduction between myself and the warm air?

To follow up, if instead of a room I was in a glass box exposed to the coldness of space but with an air temperature of 23C, would it feel much colder than in the room?

How much of the warmth I feel is due to this radiation

I would say, practically all of it.

and how much is due to conduction between myself and the warm air?

Remember that conduction to an air molecule happens very rapidly. So conduction with still air - that is, conduction to the atoms that touch you right now - will quickly reach equilibrium and heat exchange will stop.

## Use natural convection instead of conduction

Now since these heated air molecules that touch your skin are now warmer than other molecules surrounding it, they will seek upwards. They are then replaced by new colder molecules that are then been heated by conduction. This is natural convection. Whenever you are in air (or gas in general) this "conduction of many molecules in turn" is only called convection and conduction is not considered.

Back to the question: how much heating of your body is due to radiation and how much is due to natural convection.

If you want to test if convection is happening, you could hold a feather or thin piece of paper above you. Upward going natural convection might blow your feather or paper around (a little). Pure natural convection, where nothing is blowing the wind around, is usually not that big an effect. You can feel this outside on a cold summer day - standing still can actually make you feel warm, but moving is forcing your limbs through the air and forcing a convection that is not natural and much more effective.

In the case where everything in the room is at equal temperature, and has been for a while, I would expect the air to not move much around. In that case, all the radiation that your body sends out balances all the net radiation that hits your body from the surroundings. Then there is no increase in temperature. And I will argue that radiation is by far the main cause of making you feel warm.

As a side note, if we consider all the objects in the room, the walls, and your body as blackbodies (objects very good as emitting radiation) then we can consider Stefan-Boltzmann's law for all these objects:

$$I=\sigma T^4$$

$$I$$ is the intensity (energy per second per square meter, $$\mathrm{[W/A]}$$) with which objects at temperature $$T$$ emit radiation. $$\sigma$$ is the Stefan-Boltzmann constant.

All objects including walls, objects in the room, and your body emit radiation that hits and is absorbed by each other. The net amount of radiation that your body receives (which will heat you up) is:

$$I_{net}=I_{received}-I_{emitted}=\sigma T_{surroundings}^4-\sigma T_{body}^4$$

At equilibrium where your temperature is constant, $$I_{net}=0$$. So at $$T=23\: \mathrm{^o C}$$, the intensity of radiation that your body absorbs is equal to what you emit, and:

$$I_{body}=I_{surroundings}=\sigma T=5.67\cdot 10^{-8} \:\mathrm{\frac{W}{m^2 K^4}} \cdot ((23+273.15) \:\mathrm{K})^4=436 \:\mathrm{W/m^2}$$

I don't have the formula for natural convection here to compare, but I am sure this amount will be a lot bigger than the heat transfer away from your body by natural convection - and as mentioned before, at thermal equilibrium that would be even smaller (and exactly zero, if all of the air also reaches $$23\: \mathrm{^o C}$$).

To follow up, if instead of a room I was in a glass box exposed to the coldness of space but with an air temperature of 23C, would it feel much colder than in the room?

Yes! Definitely. Let's assume glass (and air in the box) is a very poor absorber of thermal radiation (which it is) that transmits all the radiation (no reflection back to your body), and that the radiation from the air and glass itself (it will emit some since it has a temperature) is negligible (does not hit you).

You still emit radiation with the above intensity, but now nothing is emitting anything onto you. You are not in equilibrium, and:

$$I_{net}=I_{received}-I_{emitted}=-I_{emitted}=-I_{body}$$

Every second you loose the above amount of heat in Joules (per square meter of your body). Loosing heat equals feeling cold. And as far as I have heard the decrease in temperature is quite rapid.

• Thank you! So it follows that to have the same level of comfort, people in houses with huge glass windows and skylights will have have to set the thermostat in winter significantly higher than people in typical houses. This also got me thinking about more efficient heating. Say you have some sort of microcoils running through your floor/ceiling/walls which allow them to change temperature nearly instantly. Then the heat could follow you from room to room while leaving the rest of the house unheated. Also would prevent heat getting wasted when warm air from a radiator pools at the ceiling. – cybrbeast Jan 24 '15 at 16:14