How do Calories (kcal) relate to watts?

Question

In thinking about exercise and "burning calories" it occurred to me that there should be some fairly intuitive correlation between the biological energy conversion going on in a person's body with the energy conversion going on in a common household object like a light bulb.

So my first question is, how can I intuitively correlate the energy usage of a light bulb with the energy used by my body?

But related to that is, what's the intuitive distinction between what watts measure and what calories measure? What's the "real world" difference between power and energy?

Answer 1

An average person uses approx. 1500-2500kcal/day. Since one kcal equals 4148J in SI units, that's between 6.2-10.4MJ per day. A day has 86400 seconds, which brings us to an average power consumption of 72-120W... about as much as a light bulb. :-)

Physical exercise varies between light (300kcal/h) at an additional 350W to very strenuous at probably six times as much, i.e. almost 2kW in chemical energy being consumed. As you can see, even light exercise will increase the metabolic rate of the human body enormously, which is good for ones health.

Since the efficiency of our muscle tissue is relatively low (18-26%), workout equipment that tells us our "power output" is usually calibrated around 15-20%, i.e. for a mechanical power output of 100W, the equipment will estimate the number of calories burned in the range of 500-600kcal/h.

This is only a rough estimate, of course. A precise measurement requires wearing a mask which can capture the CO2 that we breath out, which is a reasonably reliable chemical indicator for how much chemical energy we actually consume. The ratio between mechanical power output and chemical power consumption will vary from person to person and between different activities.

Another important way of looking at the power consumption of the human body is for environmental purposes. If we could power ourselves by sunlight directly and if the process was thermodynamically efficient, we could just about support our base metabolism by sunbathing all day long. If we could electrically recharge, we would require approx. half a dozen solar panels to get by. However, since we need chemical food sources and the synthesis of sugars, starches, protein and fatty acids in plants is very inefficient, a human being requires at least about a third of an acre of land to support his food needs by growing crops and a lot more if we want to have a diet rich in animal protein.

Answer 2

A (kilo)calorie is a unit of energy, while a watt is a unit of power, which describes the rate at which energy is expended.

So a 100W bulb is using 100 joules a second. A kcal is about 4184 joules, so a 100W bulb takes about 42 seconds to consume (really: convert into light and heat) a kcal. The joule is the SI (derived) unit of energy.

Units of energy and power used in various domains are often magnificently fouled-up and confusing although often suited to their uses: there are historical horrors like BTU, and energy is often measured in units like kilowatt-hours (so that's a thousand joules a second, for an hour, or 3,600,000 joules).

Answer 3

When you work "fairly hard", your body can produce about 200 W of power - enough for two incandescent bulbs. Top athletes can produce more - in short bursts.

Your body is roughly 25% efficient in converting "calories" (which are actually kilo calories) to Joules - meaning that if you work out hard enough to burn 600 kcal per hour, then you actually produced about 600 kJ, or 10 kJ per minute, roughly 170 W "useful output".

You can see this when you are climbing stairs. If one flight of stairs is 2.5 m vertically, then a 70 kg person needs to do about 1750 J of work to climb one flight of stairs, and will burn just under 2 (kilo) calories by doing so. This is because the calorie is equivalent to roughly 4.2 J - the energy needed to heat one gram of water by one degree Celsius.

If you want a simple translation - for a certain number of Watts of power output, the calories per hour burned are roughly 3.6 times as much (or 4x if you are into round numbers). 100 W output = 400 kcal per hour, etc.