Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!decvax!harpo!seismo!hao!hplabs!sri-unix!KING@KESTREL From: KING%KESTREL@sri-unix.UUCP Newsgroups: net.physics Subject: [Lou: Re: Why don't thermostats work?] Message-ID: <16545@sri-arpa.UUCP> Date: Wed, 8-Feb-84 13:56:00 EST Article-I.D.: sri-arpa.16545 Posted: Wed Feb 8 13:56:00 1984 Date-Received: Sat, 11-Feb-84 05:54:14 EST Lines: 58 From: Richard M. King Return-path: Received: from RUTGERS by KESTREL at 8-Feb-84 1019-PST Date: 8 Feb 84 13:19:24 EST From: Lou Subject: Re: Why don't thermostats work? To: KING@KESTREL.ARPA, physics@SRI-UNIX.ARPA cc: STEINBERG@RUTGERS.ARPA In-Reply-To: Message from "Richard M King " of 7 Feb 84 12:18:00 EST > Richard M King: > Assuming that the difference between the indoor and outdoor >temperatures is large compared to the width of the hysteresis band, we >observe that the temperature will fall at a constand rate within that band >when the furnace is off, following which it will rise at a constant rate >when the furnace is on. Yes BUT: The rates of rise and fall depend on the outside temperature. When it is colder, the house cools faster and warms slower. Thus when it is colder outside the average temperature is indeed lower. Also, since there is some delay between the time the thermostat turns on and the time the heat effectively reaches the room (due, e.g., to the heat capacity of radiators), the bottom of the hysteresis band will be lower when it's colder. However, these effects may be less significant than the other effects that have been mentioned, such as radiation and evaporation. ------- Lou, you caught me napping! Yes, there is this first-order effect that causes the minimum temperature and the average temperature in a house to be lower on colder days. I will concede incorrectness, but I will offer the following interesting second-order effect that goes the other way. The rate of temperature rise and fall are NOT constant. If the temperature is just barely cold enough to require occasional heat, the temperature will drop faster when it is near the top of the hysteresis band than when it is near the bottom. This will depress the average temperature. The temperature will RISE at a steady rate (consider the relative distances of the top and the bottom of the hysteresis band from the asymtotic temperature with the heater locked "on"). The average temperature, ignoring Lou's effect, is below the midpoint. Now take a frigid day, one where the heater is only slightly more than adequate to heat the house. This means that the asymptotic temperature with heater on is slightly above the top of the H. band, so the temperature will rise more quickly at the bottom of the band than at the top. It will fall approximately linearly when the furnace finally succeeds in shutting off the thermostat. Ignoring Lou's observation, the average temperature is ABOVE the band midpoint. Cases where the heater actually has to run ALL the time are not of interest because the thermostat has no role. Dick -------