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From: KING%KESTREL@sri-unix.UUCP
Newsgroups: net.physics
Subject: [Lou : Re: Why don't thermostats work?]
Message-ID: <16559@sri-arpa.UUCP>
Date: Wed, 8-Feb-84 13:56:00 EST
Article-I.D.: sri-arpa.16559
Posted: Wed Feb  8 13:56:00 1984
Date-Received: Sat, 11-Feb-84 07:15:03 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
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