# Turn the Heat Off!

Do you save more energy by leaving the heat on at night or by turning it down and reheating the house the next day?

- The power required to heat a house is proportional to the mean temperature difference between the house and the environment. If you can decrease the mean temperature difference, you can decrease the amount of power needed.

**A commonly held view is that you should not turn off the heat in your apartment or house when you go out, because although you may save a bit of energy, it will take even more energy to heat the space back up to normal temperature. Fact or rubbish?**

The first point to note is that whatever heat is generated inside the house will eventually be lost to the environment. The second point is that the rate of heat loss to the envronment is proportional to the temperature difference; this is Newton's Law of Cooling and it has been shown to work for houses (see An Analysis of Domestic Heating Bills). Already you might guess that this means keeping the mean temperature of the building as low as possible, for example by turning the heat off when you go out, but let's examine a real situation more carefully.

Below is a graph of temperatures inside and outside our house for one week in October/November 2007, a typical autumnal week in Vancouve, not bitterly cold but none-too-warm either. The graph runs from midnight Friday/Saturday for seven days. You can tell a lot from this graph: when we go to work (4 days a week M-Th for one of us), go to bed, get up etc. We have forced-air gas heating so it takes very little time to heat up the house, but the house cools down in a nice exponential with a thermal time constant of 1.9 days (see Task 3: Thermal Time Constant of a Single-Family Dwelling).

**Figure 1.** The temperatures inside and outside of our house in Vancouver for one week in October/November starting from Friday/Saturday midnight and running for seven days.

For this house the rate of heat loss, as shown in the gas bill experiment(see An Analysis of Domestic Heating Bills), is 9.0 kWh/day/C or 375 W/C - watts per degree of temperature difference. To get from kWh/day to kW, divide by 24. All these data, taken every minute, are in a spreadsheet (see Turn_The_Heat_Off_Data.xls) so we can calculate the difference in temperature (inside-out) for each instant in time. We can now figure out the energy loss in each time interval by multiplying the temperature difference by 375 W/C and by the 60 seconds in a minute: this gives the heat loss in Joules. Summing the entire column gives the energy loss for the week, in this case 2.77 GJ.

To estimate the heat loss if we did not ever turn off the heat, imagine the the red data points to be all at 20.5 C, the mean "heat-on" temperature. Repeat the calculation above with this new inside temperature. The weekly sum will obviously be higher than what we calculated above; it is 3.21 GJ. This is a 16% increase. Burning natural gas in the house produces about 6 tonnes of carbon dioxide per year. This is not good, but if we didn't turn the heat off when we go out or go to bed, it would be 7 tonnes, with no additional benefit to ourselves.

You can make a similar measurement yourself. It is easier if you have some means of recording temperature automatically, unless you like staying up all night.

© Physics and Astronomy Outreach Program at the University of British Columbia (Chris Waltham 2009-10-05)

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