Introduction Our model of the climate involved balancing the energy gathered from the Sun verses the energy radiated away. This is simply a balance of the energy intake of a system verses its energy output. We also considered the affect of an insulating layer, the atmosphere, on the temperature at the surface of the Earth. We will take these exact concepts and apply them to the heat balance of the human body. Homeotherms (mammals, humans) regulate their internal body temperature within a range of about 1C despite large fluctuations in the temperature of their surroundings. This is achieved by balancing the flow of heat energy. We can divide the main components of this power balance in classic physicist’s fashion (conduction, convection, radiation, evaporation) as follows
1. Metabolic rate, M
In the human body, the rate of internal energy production is called the metabolic rate. As food is broken down, and glucose is oxidized, heat is released. This oxidation process can be written in chemist’s fashion as follows
What about thinking? After spending hours studying hard, do you feel especially hungry and reward your efforts with a tasty snack? What causes this increased hunger? How much more food can you justify eating? In a recent study, participants were asked to spend 45 minutes sitting in a chair one day and 45 minutes reading an article and summarizing it another day. After they did these tasks, participants were given a survey on how hungry they were and then were given the chance to eat. It was found that when sitting in the chair, participants expended ~60 kcal and when they were reading and writing they expended 85 kcal. All participants indicated a similar level of hunger, but those who sat ate 900 kcal of food and those who studied ate 1150 kcal of food. The difference in the energy expenditure of sitting vs. studying was only 25 kcal, but the difference in the food consumed afterwards was 250 kcal [4,5]! Activities requiring significant cognitive demand favour an overconsumption of food without increased feelings of hunger. Why? Thinking requires glucose. The body keeps some glucose in the bloodstream, but stores most of it as glycogen, which it has to convert back to glucose to use. While you are thinking, your brain quickly depletes the glucose stores in your blood, and tells you unconsciously to eat so that you can return the glucose levels to normal. This results in you eating more while you study, even though you don’t necessarily feel hungry. So, next time you are studying, try to resist the urge to constantly eat, or to eat a giant snack when you do decide to visit your kitchen. If you do give in, try rewarding a long day studying by taking a break and going for a bike ride!
2. Radiation, R
The total radiation power absorbed from the environment is R. We can further decompose this term into longwave radiation from the local environment (thermal infrared from buildings, the ground, flora, and the sky) and short wave radiation from direct sunlight (visible and near infrared):
You can read more on radiation in the article on Thermal Radiation. The longwave radiation component can be calculated using the following formula:
where A is the surface area of the body, ε is the emissivity of skin (~0.98), σ is the StefanBoltzmann constant, Tskin is the (absolute) skin temperature (i.e. 306 K for bare skin) and Tenv is the (absolute) temperature of the environment. A complication occurs when we consider clothing. Clothing reduces radiation loss by lowering our effective surface temperature. However, when clothed, different parts of our body will have different surface temperatures, and we should calculate RL separately for each. Note also that in many cases Tenv is not uniform (see annotated photographs at the bottom of the Thermal Radiation article), making the application of this formula yet more complicated.
wave radiation, RS, coming from the Sun (up to ~ 1 kW/m2 or more on a clear day on an area facing the Sun directly
Fortunately when the mercury hit 54 C, the relative humidity was less than 20%, so evaporative cooling (plus a lot of acclimatization) could cope