Why is turning down the heat during day and night considered more efficient?

Question

I just want to point out right away that I am not sure if this stack exchange is the most appropriate for this question - perhaps Stack exchange Chemistry or Physics would be more suitable?

My Question

I live in Canada so our winters are pretty cold and I often hear that turning the temperature down in our house during the day (when we're away) and during the night (when we're sleeping) and only turning it back up when we need it saves energy. But I am wondering, is the following assumption correct? :

The total heat dissipated by a house will be the same regardless of the interior temperature.

This makes sense to me, the same house (same isolation, same emplacement etc...) will lose the same energy no matter if it's interior temperature is 21°C or 23°C.

Note : For this question, I am only interested by electric heating (no gas, no wood ...)

My explanation

I have a few theories as to why turning down the heat when we don't need it might be true but I would love for someone to confirm them.

1. The efficiency of electric heaters depends on the intensity at which it's running (letting it run all day at 50% might be less efficient than letting it run for a few hours at 100%) This could perhaps be related to how the metal elements resist to electricity at different temperatures?
2. The sun in the morning helps heat the house quicker and gives the illusion that it takes less energy to heat the house in the morning?

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Can someone confirm whether or not it is true that turning the temperature down in our home when we don't need it is more energy efficient and also maybe confirm or deny my hypothesis?

Answer 1

Your assumption is incorrect. More heat is lost when the difference between inside and outside temperatures is greater. So, if you keep the house at 72F (22C) it will lose heat faster than if you kept it at 62F (17C). Thus, your heater will need to run more often and/or for longer to maintain your desired temperature. It therefore uses more energy to maintain the higher set point than the lower set point.

This effect becomes more pronounced the longer the lower set point is maintained, but may not be noticeable at all for short periods. However, it's important to note that it doesn't become less efficient if you turn down the heat for short periods, since the heater is not running at all while the house is cooling to the lower set point.

Heaters (and AC) in general do not have an intensity setting - they're either on or off. The energy from the sun does play into things a little bit, but not a whole lot and not really in the morning. Opening curtains during the day can certainly help to make the house feel warmer.

All of these effects apply in the summer, too, although then you want a higher set point when you're not home, not a lower one, close curtains during the day, etc.

Answer 2

The total heat dissipated by a house will be the same regardless of the interior temperature.

Nope. Actually, thermal transfer is proportional to the difference in temperature.

This is the base presumption on which everything else is built, so they all topple like a house of cards at this point.

We see this a lot. It's a rationalization. The underlying motive is to leave the heat/AC up all the time, so the house is comfortable when you come home. The real answer is "get a Nest".

The efficiency of electric heaters depends on the intensity at which it's running

Nope, not that either. Electric heat is 100% efficient because the only energy exit is heat, and there's nowhere else for the heat to go but your house. (Mind you it's possible to botch this up, e.g. Putting a baseboard heater on an exterior wall, making the wall 45C and thus pushing a lot of the heat through the wall).

Generally all electric use becomes heat, unless it shines photons out a window, or drives an endothermic chemical or isotopic conversion e.g. A battery. The only exception is Bitcoin mining etc., which becomes heat and money.

The sun in the morning

Yup, this helps. Houses designed to exploit this are called passive solar homes.

Answer 3

To answer the query about why the heat flow into or out of the house is proportional to the difference in temperature, it is a case following the equations for heat flow which we have found experimentally to be true for a wide range of physical situations.

The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. https://en.wikipedia.org/wiki/Thermal_conduction#Fourier.27s_law

A related formulation of this property is Newton's Law of Cooling.

Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings provided the temperature difference is small and the nature of radiating surface remains same.

As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant. This condition is generally true in thermal conduction (where it is guaranteed by Fourier's law), but it is often only approximately true in conditions of convective heat transfer, where a number of physical processes make effective heat transfer coefficients somewhat dependent on temperature differences. Finally, in the case of heat transfer by thermal radiation, Newton's law of cooling is not true.

Sir Isaac Newton did not originally state his law in the above form in 1701, when it was originally formulated. Rather, using today's terms, Newton noted after some mathematical manipulation that the rate of temperature change of a body is proportional to the difference in temperatures between the body and its surroundings. This final simplest version of the law given by Newton himself, was partly due to confusion in Newton's time between the concepts of heat and temperature, which would not be fully disentangled until much later.