Thermodynamics. Thermostats.

Originally was going to post this in off topic, but since it applies to vehicles too, here we are. 

The wife and I have the same dispute every winter. She says keeping the house colder conserves on the electric bill. I say it doesn’t matter. 

My reasoning is, if it is 30° outside, and the house is set to 70°, then the thermostat will kick on, run until the house is say 71°, then kick off until it is something like 69°. 

So, when she wants to set it to 65°, it really makes no difference, since the thermostat does the same thing, and the heaters run for the same time, the only variable being the set point and the thresholds for “too much” and “too little”. Right? 

Im talking house thermostats, but a thermostat for a radiator fan does the same thing right? 

Prove my sanity. 

the rate of heat exchange between two bodies (ie the house and the atmosphere) is directly proportional to the difference in temperature between them.

so if we assume that the outside temperature is 30, it does indeed cost more to keep the thermostat at 70 versus 65, because you lose more heat to the atmosphere at 70 than you do at 65.

if the "on" and "off" events are still triggered by the same delta from target (ie the +/- 1 degree "on at 69, off at 71" you used), the difference will be that it will run more frequently at 70 vs 65, and it will also run longer because the loss rate is higher.

The difference between the inside temp and the outside temp is what drives the heat flow through the wall. Greater difference, greater heat flow; the longer the furnace will run each time it cycles on and it will probably run more often too.

These guys get it. I hate to say it, but you're gonna have to concede this one to SWMBO. 

They’re right man. The closer you are to the outside temp the cheaper it is to maintain that temp. 

To use a car radiator fan analogy, consider that the job of that fan is to cool, and that fan will have to spend more time running in summer driving than winter driving. Same thing, just in reverse. The car's radiator is like the surfaces of your house, except that it conducts heat very quickly instead of very slowly (since you generally want to keep the heat/cool in your house, while you want to dump heat out of an engine as quickly as possible).

Your wife is right.  However, I tell mine that we work hard so that we can live in a heated shelter and if I'm cold I'm just going to turn up the heat.  Fortunately, if I'm cold she's freezing so I can get away with that particular pronouncement. 

Entropy is always increasing.

  Heat flows from hot to cold.  

Bigger temperature differential means it takes more energy into the system to raise the temperature.

I don’t mind being wrong. I just wanted someone to make sense of it to me. I know a little thermodynamics, but did not know that the further you are away from a constant temp, the faster the area in question will try to get back to that temp. I always thought the rate at which a degree drops is steady, given a constant low. 

Now I know, “and knowing is half the battle!”

Yep, they're all correct.  Moving to the car part, on a cold day your car can give off the excess heat more easily so it doesn't overheat (big temperature difference means more heat loss).  But in the hot summer, it doesn't give off as much heat (because the temperature difference is smaller) and it overheats.

APEowner said:

Your wife is right.  However, I tell mine that we work hard so that we can live in a heated shelter and if I'm cold I'm just going to turn up the heat.  Fortunately, if I'm cold she's freezing so I can get away with that particular pronouncement. 

Lucky you! My wife and I are polar opposite, most of the time. 

The wife is right.

According to the DOE, every degree is worth about 3% on the electric bill. Source.

You can demonstrate this with a cup of hot water and a thermometer. 

If you measure the temp of the water vs. time, you’ll find the temp drop slows as you approach room temp. 

The thread about HF vs Yeti mugs may already have data showing how temp difference affects cooling rate even with good insulation. 

dculberson said:

They’re right man. The closer you are to the outside temp the cheaper it is to maintain that temp. 

What he said