Why Does a Room Get Hot When People Gather?
― Each Person Gives Off About 100 Watts of Heat, Like a Light Bulb
Even sitting perfectly still, your body keeps giving off about 100 watts of heat. In a classroom of 35, that equals three electric heaters. And the air in a room warms up with far less heat than you might think.
On a winter morning, an empty classroom feels chilly. But by the end of first period, with everyone in their seats, the windows are fogged up and the air feels stuffy.
The heating setting hasn't changed. The temperature outside has barely moved.
The only thing that changed is the number of people in the room. So how much heat does a person actually give off?
Just two reasons
Nearly all the energy we take from food ends up leaving the body as heat. Even sitting still, that is about 100 watts.
Air is light, so it takes only a little heat to warm it. The heat that warms a classroom's air by 1°C would warm only about 55 litres of water.
Put a big source of heat together with a container that warms easily, and the room's temperature rises noticeably just because more people are in it. Let's take it step by step.
Where do the 100 watts come from?
An adult eats roughly 2000 kilocalories of energy a day. Divide that by the number of seconds in a day and you get about 100 joules per second. 100 joules per second is what we call 100 watts.
The body uses this energy to keep the heart beating, to breathe and to stay warm. But unless it does work on something outside itself, the energy it uses finally leaves the body as heat. So a person gives off about as much heat as one old-style incandescent bulb, even while asleep.
Moving makes it more. Walking gives two to three times as much, and hard exercise is said to give nearly ten times as much.
So what happens as more people come in? Look at Figure 1. The slider changes the number of people in the room.
Why does air warm up so quickly?
The air in one classroom weighs about 230 kilograms. It looks big, but there is not much in it.
On top of that, air warms by 1°C with only about a quarter of the heat that the same weight of water needs. Because it is light and warms easily, even a whole classroom of air can store only as much heat as about 55 litres of water.
Pour 3500 watts from 35 people into it, and the air alone would warm by 1°C in about a minute. In reality, the walls, desks and floor soak up most of the heat, and ventilation carries some outside. Even so, a rise of a few degrees over a one-hour lesson is said to be common.
Why does it feel muggy, not just hot?
Body heat has three exits. Look at Figure 2.
Evaporation, the bottom exit, is heat carried away when moisture leaves through breath and skin. This heat does not move the thermometer; it raises the room's humidity. Windows fog up in a crowded room because this moisture turns back into water on the cold glass.
So when people gather, temperature and humidity rise together. That stuffy feeling is the two combined.
People who design cooling for buildings always ask how many people will be in a room. They count how many watts of heat and how much moisture each person gives off, and size the cooling from that. In packed halls and trains, the air conditioning can be running even in midwinter.
Summary
The human body is a heater of about 100 watts that turns the energy it eats into heat. Room air is light and stores little heat, so the temperature rises as soon as people gather. Part of the heat leaves as moisture, so humidity rises too.
A person is a walking 100-watt heater.
Gather 35 people and it is the same as having three electric heaters switched on.
For the organ that uses a fifth of the body's energy, see "Is it true that thinking makes you hungry?". For how the body makes more heat when it is cold, see "Why does your body shiver when it's cold?".
- Put a thermo-hygrometer, which shows temperature and humidity, on a table in the middle of a room.
- Note the temperature and humidity while you are alone. Then, after family members have gathered for about 30 minutes, note them again.
- Keep the heating and the windows the same. Compare which of temperature and humidity changed, and by how much.
The smaller the room and the more people there are, the clearer the change. In winter, also watch how the window glass fogs up.
For those who want to know more ― terms, formulas and links to textbooksEach part is labelled by level, from middle school science to university courses
- Middle schoolCovered in middle school science
- High schoolCovered in high school "Basic Physics" and "Basic Biology"
- High school+Advanced high school material, or textbook sidebars
- UniversityUniversity specialist courses (environmental physiology, building services engineering), not covered in high school
- ResearchNot yet settled even at university level; researchers are still studying it
Middle schoolTerms: this phenomenon has names
- Watt (power): the amount of energy flowing per second. One joule per second is one watt.
- Heat capacity: the amount of heat needed to raise something's temperature by 1°C. It is larger for heavier things and for materials that warm up slowly.
- Basal metabolism: the energy used just to stay alive, even when lying down doing nothing. For adults it is said to be about 1200 to 1500 kilocalories a day.
Middle schoolHigh schoolCheck it with a formula: how many seconds for the air in a 35-person classroom to warm by 1°C?
We work out one person's heat from the amount they eat, then calculate how many seconds it would take to warm the classroom air by 1°C. Heat absorbed by walls and furniture, and ventilation, are ignored here. The units are joules (J) for heat, seconds (s) for time, and watts (W) for the rate of heat output.
| In symbols | t ＝ ( ρ × V × c × ΔT ) ÷ ( N × P ) |
| In words | Time taken ＝ heat needed to warm the air ÷ total heat the people give off per second |
| Where it comes from | Conservation of energy. We assume all the heat the people give off (N × P × t) becomes the temperature rise of the air (ρ × V × c × ΔT). One person's heat P is found the same way: P ＝ a day's food energy ÷ seconds in a day. |
| Symbol | Meaning and unit |
| t | Time for the air to warm by ΔT (seconds) |
| ρ | Density of air (kilograms per cubic metre) |
| V | Volume of the room (cubic metres) |
| c | Specific heat of air (heat to raise 1 kilogram by 1°C, in joules) |
| N | Number of people in the room |
| P | Heat given off by one person (watts) |
| Food energy an adult eats in a day (rough guide) | 2000 kcal |
| 1 kilocalorie in joules | 4.184 kJ |
| Seconds in a day | 86400 s |
| Classroom size | 8 m × 8 m × 3 m high |
| Density of air (around 20°C) | 1.2 kg/m³ |
| Specific heat of air | 1000 J/(kg・℃) |
| Specific heat of water | 4.18 kJ/(kg・℃) |
| A day's energy in kilojoules | 2000 × 4.184 ＝ 8368 kJ |
| Convert to joules | 8368 × 1000 ＝ 8368000 J |
| Per second (one person's heat P) | 8368000 ÷ 86400 ≒ 96.9 W |
| Total for 35 people (taking P as about 100 W) | 35 × 100 ＝ 3500 W |
| Classroom floor area | 8 × 8 ＝ 64 m² |
| Classroom volume V | 64 × 3 ＝ 192 m³ |
| Mass of air (ρ × V) | 192 × 1.2 ＝ 230.4 kg |
| Heat needed for 1°C (ρ × V × c) | 230.4 × 1000 ＝ 230400 J |
| Time for a 1°C rise, t | 230400 ÷ 3500 ≒ 65.8 s |
| Water warmed by the same heat | 230.4 ÷ 4.18 ≒ 55.1 kg |
For the air alone, 35 people would warm it at a pace of 1°C every 66 seconds or so. Even a classroom full of air can store only as much heat as a few buckets, about 55 litres, of water. The real rise is much slower because walls and furniture have far more heat capacity than air and take in most of the heat.
High schoolHigh school+Why does the body turn energy into heat?
High schoolThe body breaks down sugars and fats from food by respiration, and first transfers that energy to an "energy currency" inside the body before using it. This transfer is only about half efficient, and the rest becomes heat on the spot. The energy that is used also ends up as heat unless the muscles do work on something outside, such as lifting an object.
High school+One person's heat output depends on body size. Heat per unit of body weight is known to be larger in smaller animals, and there is a rule of thumb, Kleiber's law, that metabolism scales with body weight to the power of three quarters. So a classroom of children and a meeting room of adults differ a little in heat per person.
UniversityThe human heat balance equation and air-conditioning heat load calculations
In environmental physiology, the body's heat balance is written as the "human heat balance equation". It says that the heat made by metabolism, minus work done on the outside, equals the sum of heat lost by radiation, convection, conduction and evaporation, plus heat stored in the body. Fanger's comfort equation and the Predicted Mean Vote (PMV) use this equation to predict how hot or cold people feel. In building services engineering, heat from the body is split into "sensible heat", which raises temperature, and "latent heat", which leaves as moisture, and both go into the heat load calculation. The evaporation share in Figure 2 is this latent heat.
📖 Derivations and further reading: Heat capacity (Wikipedia, in Japanese) ／ Basal metabolism (Wikipedia, in Japanese)
ResearchWhat is still not clear
- Whose body should set the comfortable room temperature? Office temperature standards are said to have been based on the metabolism of a man around 40 years old, decades ago. A 2015 paper pointed out that women's metabolism is lower, so they tend to feel cold at the standard temperature, and the debate continues.
- Even with the same build, heat output differs between individuals. Basal metabolism cannot be explained by body size alone, and about 10% individual difference remains. How much muscle mass and special heat-producing fat (brown fat) account for it is still being studied.
- Air flow when people gather. Warmed air rises around each body. How these flows overlap in a packed room, and where it gets hottest, needs calculation or measurement for each room.
In other words, this article too is an explanation of "what is known so far". Treat the figure of 100 watts as a rough guide that goes up or down with build and activity.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science: "Electric power and heat" and "Conservation of energy" | Watts and joules, calculating amounts of heat |
| High school | Basic Physics: "Heat and energy"; Basic Biology: "Metabolism" | Specific heat and heat capacity, heat from respiration |
| High school+ | Advanced biology (body size and metabolism) | Kleiber's law |
| University | Environmental physiology, building services engineering | Human heat balance equation, sensible and latent heat, heat load calculation |
| Research | Thermal comfort research | Comfortable room temperature standards and individual differences |
| ― | Links to daily life | Ventilating crowded rooms, heating and cooling settings, fogged windows |
- Ministry of Health, Labour and Welfare (厚生労働省), "Dietary Reference Intakes for Japanese (2020 edition)" (basal metabolic rate reference values and estimated energy requirements)
- Society of Heating, Air-Conditioning and Sanitary Engineers of Japan (空気調和・衛生工学会), "Handbook of Air-Conditioning and Sanitary Engineering" (heat output of the human body)
- ASHRAE Handbook—Fundamentals (chapter on Nonresidential Cooling and Heating Load Calculations, heat from people)
- Kingma, B. & van Marken Lichtenbelt, W. (2015) Energy consumption in buildings and female thermal demand. Nature Climate Change
- Wikipedia, "Basal metabolism" (基礎代謝, in Japanese)
※This article is a general-audience science explanation. The figures given are rough guides to help you understand how things work. Heat per person varies greatly with build, age, activity and clothing.