Room heating energy:
how much heat a temperature rise takes

The three-factor sum

Warming a substance takes heat in proportion to how much of it there is, how much it resists warming and how far the temperature has to go. Those three ideas are mass, specific heat and temperature change, and multiplying them gives the energy.

Water has one of the highest specific heats of common materials, which is why it stores and carries heat so well in tanks, radiators and underfloor systems.

Heating the air in a room

To warm the air in a room, first convert the volume into mass using the density of air, around 1.2 kg/m³ at typical room conditions. The specific heat of air is roughly 1.005 kJ/(kg·K), a quarter of that of water.

That is surprisingly little. A 2 kW heater, 2 kJ per second, would take 1,809 ÷ 2 = about 905 seconds, a little over 15 minutes, to supply it with no losses at all.

The air in a room is only a small part of what needs to be warmed, and a real room takes far longer, which the next section explains.

Why real rooms take longer

Walls, floors, furniture and ceilings hold far more heat than the air, and they absorb a large share of what the heater supplies. A concrete floor and brick walls may hold hundreds of times the heat capacity of the air. Meanwhile heat leaks out through walls, windows and ventilation while you warm the room.

For that reason, the m × c × ΔT figure for the air is a minimum, and a practical estimate uses heat-loss figures and a heater rated against the losses instead.

Specific heat of common materials

The value of c differs a great deal between materials, which explains why some things warm up quickly and others hold heat for hours. Typical figures are listed below; use data for your own material where precision matters, because composition changes the number.

Per kilogram, water takes more than four times the energy of air for the same rise. Per cubic metre the difference is far larger, because water is about 800 times denser than air, and that is why a small tank can carry as much heat as an enormous volume of air.

From kJ to kWh and running cost

Electricity is billed in kilowatt-hours, so convert kilojoules by dividing by 3,600. The 1,809 kJ for the air is 0.50 kWh, and the 4,180 kJ for the water is 1.16 kWh. Multiply by your unit price to cost it.

An appliance cost tool applies a tariff to the kWh figure, and an energy tool converts watts and hours into kWh, so they are practical for the final step. A heat pump or a heat-recovery system changes the electricity needed per unit of heat, which is why coefficient of performance matters.

Choosing a heater for the job

The power of the heater sets how fast the energy arrives, and the losses set how much power is needed just to hold the temperature. A practical selection therefore needs two numbers: a steady-state loss at the design temperature difference, and a warm-up margin to bring the room up in the time you accept.

1. 1Estimate the steady loss in watts through walls, roof, floor, glazing and ventilation.
2. 2Add the warm-up energy for the air and for the fabric, divided by the time you allow.
3. 3Choose a heater rated at or above the sum, rounding up to a standard size.
4. 4Check the electrical supply and the cost of running it for the hours you will use it.

A quick check with the sum above shows whether the heater is in the right order of magnitude, but the final selection should follow a heat-loss calculation for the actual building and a recognised design method.

Assumptions worth stating

The formula assumes a constant specific heat, no change of phase and no heat loss. Over a narrow range of temperature these are fair for water and air. Moisture in the air, humidification or boiling would need extra terms.

• Specific heat values are approximate and shift slightly with temperature.
• Air density depends on temperature, altitude and humidity.
• The sum gives energy delivered to the material, not the energy bought, which depends on the efficiency of the heater.
• Heat loss over the heating period is additional and often larger than the sum itself.

Slips to watch for

Mistakes in heating sums tend to come from units and from forgetting what has been left out. Kilojoules and kilowatt-hours differ by a factor of 3,600, and degrees Celsius and kelvin share the same step size, so confusing them in a difference does no harm, but using kelvin values in place of a difference does.

Another slip is to treat the air-only figure as the heater's job. The result of about 1,809 kJ for a 150 m³ room looks tiny, yet it ignores the thermal mass of the building and the continuing losses. If a heater of the apparent size struggles in practice, the explanation is almost always the fabric and the leakage rather than a fault in the heater.