• How much power will a human body (area 1 m2) radiate in a very warm (298 K or 25°C) smoke filled room emit if normal skin temperature is 306 K (33 °C). Would a thermal imager be of any use if there were a freak fire were inside a turkish bath house (temperature 40 °C) or a sauna complex (temperature 80 °C)? Assume that the emissivity of the body and its surroundings are both 0.95.

For any situation where there are significant amounts of both emitted and absorbed radiations then we should use the following equation:

.

For the body in the smoke filled room:

For the turkish bath house:

That is, the body is absorbing a small amount of energy by radiation.

For the sauna complex:

Here the body is absorbing a large amount of radiative energy.

However the question is would a thermal imager be of any use in these situations? For the smoke filled room clearly it would be, if only because we know that that is precisely what fire fighters use to find unconscious victims in smoke filled rooms. It should be realised though that the imager will detect the full, not the net emission from the body but that it will be seen against a background that is also emitting. Since the room is slightly cooler than the body and has the same emissivity it will appear darker through the imager.

In the turkish bath the body will be slightly cooler than the surroundings and so it might seem that body would appear slightly darker in the imager. In the sauna though the body at the stated temperature would be much cooler than the surroundings and so would appear much darker than the surroundings.

There are two complications though. Firstly what would the skin temperature of a body in a turkish bath or a sauna really be? The human body is very good at regulating its core temperature but skin temperature can vary greatly, depending on the environment. You have not been presented with enough information to fully evaluate this effect. A more important point though is nature of the infrared radiation that the imager uses; IR will penetrate smoke as if it were not there, since the smoke is largely transparent to IR. However water vapour is an excellent absorber of IR (this is why on a sunny summer's day you suddenly feel much cooler when even a light wisp of cloud passes in front of the sun), and so the IR image of the body will be completely blocked in the steamy environment of a turkish bath. A sauna has a lower relative humidity but the total amount water vapour is still likely to be high enough to block the imager's view.