[Physics] Does it require more energy to maintain higher temperature in the same environment

energythermodynamics

Let's say you have a house with natural gas atmospheric heater water radiator system. Does it matter in terms of natural gas expenditure, if the house is kept at higher or lower temperature, assuming the outside temperature is always lower than inside?

Let's say you have the thermostat which regulates the heating system to keep more or less constant air temperature. You are leaving the house for a number of days. The common wisdom is to turn down the heating system to lower temperature so that it somehow saves energy.

However, unless you can completely turn the system off for the duration of your absence, does it matter, if the thermostat is kept at 15°C or at the 21°C you use when you are in?

Quite possibly I am wrong here, my instinct was that the house loses heat at a more or less constant rate, which is independent of the inside temperature of the house.

At the start of your absence, the inside of house is broadly at 21°C. If you turn the thermostat to 15°C upon leaving, there will be no gas spent during the time house cools down. Then the gas spent to maintain 15°C will be about the same amount as to maintain 21°C. Then when you return, you have to heat the house up and you expend the energy you saved during cooling, to heat the house back up.

Is it right or am I missing some basic physics here? Or perhaps it is dependant on actual temperature differences between inside and outside?

Best Answer

I'm afraid your instinct is wrong, thermal transfer rate is very much dependent on the thermal gradient. In a given environment, hotter things cool at a faster rate.

It's quite easy to test this. Make two cups of coffee. Add cold milk to one immediately, and the same volume of cold milk to the other one after two minutes. Measure their temperatures. You will find that the second cup has cooled considerably faster than the first, as the coffee was hotter.

Equivalently, you could do the reverse. Maintain the temperature of your house at a steady 21°C. Then measure your energy usage to maintain that temperature at different outside temperatures. You will find (instinctively) that the colder it is outside, the more energy is required to maintain the internal temperature.