Making Sense of Heating Cost

Body heat is retained when using sleeping bag: A self-heating technology.

Living in Canada means surviving in very cold winter, unless you live in Vancouver or surrounding areas abutting Pacific Ocean. Canadian winter is harsh; temperature can dip to below -20°C regularly and it's been said to make Canadians strong quiet type. In the province of Ontario, it is slightly milder, about -10°C but the wind is fiercer. In Alberta, we get chinook ("snow eater") wind every 2-3 weeks, so the temperature can change from -20° to 5°C in a day and a week later it will drop to -20°C again.

At a household level, the winter means Canadian families need to spend money to heat their houses. Typically, a house is kept at about 21°C to make everyone feel comfortable (i.e., not wearing sweater at home), so there could be a 50°C temperature difference between inside and outside the house. The monthly heating cost can range from $90 in summer to $200 in winter. What is interesting is that most of this heating cost comes from administrative (30%) and delivery (30%) charges.

It is also interesting to notice that the retail natural gas price in Canada remains low, at about $4/GJ. (GJ = Gigajoule = 10⁹ Joule; Joule is a unit of energy, named after James Prescott Joule). How can I say $4/GJ price cheap? An old, energy-hungry fridge typically needs 639 kWh per year = 2.3 GJ per year. This means natural gas priced at $4/GJ could power this fridge for one month for less than $1. Another benchmark I can compare to is the electricity price in Canada, which is 8 ¢/kWh. The natural gas price of $4/GJ is equal to 1.4 ¢/kWh. It is not surprising Canadians are not that interested in energy-saving measures. It's the economy, stupid.

Note: A more familiar unit of energy is Watt (named after James Watt). 1 Watt = 1 Joule per second, so that 1 kWh = 10³ W × 3600 seconds = 3.6 × 10⁶ J = 3.6 MJ. (MJ = Megajoule.)

When the administrative and delivery charges are included, the natural gas price becomes roughly $8/GJ. The energy needed to heat an average-sized house per month is roughly 24 GJ in winter; thus the cost is about $200/month in the winter. Okay, so the numbers add up and we now understand our monthly natural gas bill.

The household 24 GJ/month heating budget is to compensate mostly for thermal radiation and convection heat loss from the house to outside. Thermal radiation loss from a house is proportional to the surface area of the house in contact with the outside. The larger the house, the larger the area becomes. A typical house in Canada has a surface area of 300 m². Using the Stefan-Boltzmann law,

ΔP = 4 ε σ A T³ ΔT,

we can figure out the amount of thermal radiation loss ΔP which depends on emissivity ε and outside temperature T (say, -23°C = 250 K). ΔT is the temperature difference which is about 7°C (roughly the difference between the exterior wall's and the outside's), while σ is the Stefan-Boltzmann constant. (Emissivity ε of the house exterior wall can be assumed to be 1, so we don't need to worry about it.) The numbers work out to be ΔP = 7.0 kW, or 18.1 GJ/month.

In addition to heating the house, we need to heat water for shower as well. The heat capacity of water is 4200 J/kg per degree Celcius. A person can use water up to 160 litre = 160 kg per shower. Considering a more environmentally committed family, a family of four might use about 450 litre for shower, cooking, and washing dishes. Canadians shower once a day, so the amount of energy needed to heat the water from 10°C to 60°C is about 95 MJ. In a month, it will be 4 GJ when factoring furnace efficiency. The water heating energy budget is about 17% of the total 24 GJ/month

The remaining 1.9 GJ/month could be attributed to convection loss and thermal contact loss with the ground.

The 7 kW heat emitted by a typical house is a waste heat. Your house is a light bulb, LOL. Your carbon footprint. This heat can be tapped and converted into electricity, but thermoelectric technology is not cheap.