[Eternal Student (OP)]

Hi.

   So how much does the entropy of the universe change just when a roof tile falls off a roof that was 10 metres above the ground?   Specifically, the final state of our universe is taken to be when the tile has hit the floor and all energy has been dissipated in the usual ways.   The starting state was where the tile was at rest 10 meters up and let's say it was perched on the edge ready to fall off with the slightest bump or vibration - a vibration we can ignore for our purposes of energy considerations.    Other than the tile, there weren't any other significant changes in the universe over that time we need to consider  (I know that's unlikely - I'm just interested in the entropy change due ONLY to the tile falling because there's precisely nothing we can do about the entropy changes due to some far away astronomical phenomena but roof tiles, that's a different thing - we CAN make sure we don't do any roof tiling at certain times of the year).

    Anyway, this sort of thing gets mentioned in a few textbooks on Thermodynamics.    The change isn't a reversible process but we can reach the final state from the initial state through some series of slow and reversible changes without much trouble.   All we need to do is make sure we do have the same initial and final states.   So at the end we have a static tile on the floor and some heat released into the surroundings.   In the beginning we had a static tile in the air BUT it had potential energy  mgh =  10mg.   We can devise various reversible processes where we slowly lower the tile down and pass all the energy  mgh   to a heat reservoir.   For simplicity the environment locally to the tile,  let's say within a couple of miles of the tile can be taken as a suitable heat reservoir.  We can pass all the heat to that and the temperature of it doesn't really change.   That's also good enough for our requirement that the end state has the heat in the surroundings,  it's more or less all in the first couple of miles of the tile.   So we get a rough estimate for the change in entropy of the universe  =  ΔQ_rev / T   =   mgh / T.

   Now the thing is,  T appears in that formula and we took T to be the temperature of our local heat reservoir  (the local surroundings of the tile).   Does this mean that the entropy change of the universe is higher when the tile falls on a cold day and lower on a hot day?
   Should we save the universe from ultimate heat death by insisting that builders only undertake roof repairs on a hot day?   More generally, since every process we undertake ultimately delivers some heat to the environment, should we just restrict all major activities to the hot days?
   Anyway, first things first,  the change of entropy for the local area does seem to be dependant on the ambient temperature of the day.  That much I can go along with.  However, does this really hold out if you extend out to the entire universe and leave enough time for the heat to fully dissipate out to everywhere?   Is the entropy change of the universe really less if the tile falls on a day where the temperature local to the tile was high?
    (I don't know....  I've just been re-reading an old textbook and I never really stopped to question it carefully when I was younger).

Best Wishes.

[alancalverd]

The biggest entropy increase was incurred in the manufacture  of the tile.

Buty whilst it is certainly true that more energy is dissipated by its falling on a cold day than a hot one, the hot day will eventually cool down towards the 3K of the rest of the universe so energy is conserved, ΔS > 0, and all's right with the laws of physics even if the immediate environment is going to hell in a handbasket.

[Eternal Student (OP)]

Hi.

    Yes, that's pretty much what I started thinking just before I went sleep. I doubt I would have found this by trying to use Google with some well chosen search terms and the postman wasn't really sure about it this morning.  It's very reassuring to hear someone else voice the same sort of idea,  so thank you very much for your time.   

This is roughly how I was going to phrase things to the next visitor:
    The universe really did have it's entropy change kept small when the tile fell on a hot day - but it was only for that moment of time (let's say for that day).....  When the hot day(s) end and the local region around the tile cools to typical temperature, all that heat is just dissipated to the universe at whatever temperature it is (about 3k based on the CMB).  When that happens, the universe gets a faster than average increase in entropy and that extra little bit of energy (mgh) makes it's contribution just like any other heat energy that was around in the local region of the tile.
     To say it another way, it wouldn't matter if the tile had fallen on a cold day provdied you determine the change in entropy of the universe by taking the time averaged entropy of the universe (over a long enough period of time so that several hot and cold days have come and gone local to the tile) and consider that with and without the event of the tile falling on the first day.  It's only the same day's entropy of the universe that is affected by the temperature that was just local to the tile on the day it fell.

Best Wishes.

[Halc]

I could argue that the time makes no difference in the long run, falling on a hot or cold day, or not falling at all.
Energy pours into the Earth system, mostly via sunlight. All that energy is lost eventually to entropy. Such things as tiles falling or being put up there in the fist place are only perturbations in this general curve, perturbations which are not chaotic and tend back towards the main line just like any pendulum. So the universe will not be saved at all by doing your work on hot days.
On the other hand, I have an asphalt roof and it needs to be done near a hot day to seal properly. Roofs put up in winter tend to fail years earlier.