Science For Everyone - The Heat of a Candle, and of You

Copyright © Karl Dahlke, 2023

A candle generates 100 watts of power, mostly heat, and a little bit of light, when it burns. 🕯 You dare not put your hand directly over the flame; you will get burned. In fact, a candle can keep a small fondue pot on the boil, and such pots can be purchased today.

A human being, such as yourself, generates 100 watts, just sitting on the couch. The heat escapes into the room across your entire body. It is not concentrated at a single point, like the candle, but the energy output is the same. Three people and two candles in a room is the same as five people, or five candles.

A friend told me that he ran into hard times a couple years ago, and found himself without power in the winter. He bought a dozen candles and used them to heat up one room of his apartment. Is this feasible? If anything, the goal of this book is to help you answer questions of feasibility whenever they appear, especially if they come from politicians, or social media.

Suppose he has twelve candles burning in a closed room. That's 1,200 watts. What if the power was on and he had a space heater instead? A standard electrical socket delivers 110 volts, and can support up to 15 amps. Multiply these together and get 1,650 watts. A space heater could, in theory, deliver 1,650 watts without blowing a fuse. In practice they run closer to 1,200 watts. A hair dryer on high is also 1,200 watts, as is a toaster. Therefore, twelve candles could heat a room, just as a space heater could heat a room. However, it's not quite the same. A space heater blows the heat directly on you, and the space around you, whereas the heat of a candle rises up to the ceiling. So it would take a couple more candles, or a little longer, to heat the room by flame. And of course there is the ever-present risk of fire. You can fall asleep in front of a space heater (with modern safety features), you dare not doze off surrounded by candles.

If you have a large extended family, you can achieve the same effect by cramming 15 people into a small room.

Wrapped Person

Suppose a person were wrapped in insulation, so that every square inch of skin was covered. In other words, no heat can escape. Yes, there is a small hole through which he can breathe, and some heat escapes through his exhalations, but as a good approximation, we can say that no heat escapes. How long will he live?

Body temperature is 98.6 fahrenheit, or 37 celsius. This is our starting point. A human usually dies of heart failure at 105 fahrenheit, or 40.5 celsius. An increase of 3.5 degrees proves fatal.

Remember that a person generates 100 watts of heat, which in our fantasy, cannot escape. To keep the math simple, let's say he weighs 100 kilograms, or 220 pounds. 100 watts dumps 100 joules of energy into 100 kilograms of mostly water, every second. That's one joule of energy into each kilogram of body tissue, every second.

One calorie of heat raises one gram of water one degree celsius; that's the definition of a calorie. There are 0.239 calories in a joule. Thus each joule raises each kilogram of bodily fluid 0.000239 degrees. Every second, his body temperature increases by 0.000239 degrees. Divide this into 3.5 degrees and get 14,644 seconds. There are 3600 seconds in an hour, thus he can only live in this cocoon for 4 hours and 4 minutes.

Calories per Day

The food industry has introduced a new and slightly confusing unit, the Calorie, with a capital C. This is a thousand calories, or if you prefer, a kilocalorie.

Look at the nutrition facts on a candy bar. If it claims 100 Calories, that means it provides 100 kilocalories, or 100 thousand calories, of energy to your body. You will obtain this much energy after digestion if you eat that candy bar.

With this in mind, how many Calories do you need each day? How many Calories should you eat to be healthy, without gaining weight?

As always, I will make several simplifying assumptions. We're only looking for a rough estimate here.

Let's say you don't do any exercise. Aerobic exercise can push your metabolic rate up to 3 or 4 hundred watts, and an athlete can do this for several hours. But you are just going through your day.

You burn, and require, 100 watts, times the number of seconds in a day. That's 100 × 24 × 60 × 60 = 8.64 million joules. If you want to carry the units along, which is always a good idea, you have 100 joules per second (a watt is by definition one joule per second), times 24 hours per day, times 60 minutes per hour, times 60 seconds per minute, is 8640000 jhms over dhms, or 8.64 million j/d, or 8.64 million joules per day. Multiply this by our conversion factor of .0239 calories per joule, 0.239 c/j, to get 2.06 million calories. But these are calories, not food Calories. Divide by 1,000, and get 2,000 Calories per day. This is the accepted average. A person needs 2,000 Calories per day to survive, and should not eat much more than that, else he starts to gain weight. As mentioned earlier, there are many factors that are not addressed here, such as exercise. Please consult a doctor or a dietician when determining what to eat, and how much to eat.