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Is it possible to measure the passage of time by simply timing the melting of a block of ice of a known mass and temperature, in a room of a known size and temperature?

Given that today we still refer to refrigeration in units of "tons of ice," my thought is that if you accurately knew the temperature inside a room wherein 4 tons of ice at 32°F, for example, was melting, you can accurately measure the passage of time by using nothing more than a thermometer.

It would appear to be a logarithmic function of temperature, but what would such a calculation look like? Assume we are given mass of the ice, temperature of the ice, volume of the room, air pressure (or simply mass of the air being cooled), and the temperature readings of the room over some regular interval beginning at t=0. Also assume the room is sealed and very well insulated, with no circulating fans. Also the volume of the insulated wall being cooled can be considered negligible to the required accuracy of the timer.

How could one use this information and material to calculate an accurate passage of time - for example build a timer - which would trigger upon a precise and predictable time by means of a switch connected to the room thermometer (a bimetallic coil, I assume)?

The end goal is being able to begin with a fixed room of known temperature, and introduce a mass of ice sufficient to trip at some very predictable future time based on nothing but the melting of the ice.

I have looked through a similar question which involves heaters and different assumptions, which doesn't seem to resolve itself to answering a function that can predict a volume of ice per unit time. That question is here and may provide some reference material.

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    $\begingroup$ How do you guarantee a constant heat transfer rate into the ice? Under the best conditions, I would expect the heat transfer rate to vary with surface area, which will constantly be changing as the ice melts. $\endgroup$
    – David White
    Oct 2, 2020 at 17:47
  • $\begingroup$ well i don’t exactly know but for consistency can we assume the block will begin as a cube, whatever the mass? how does the refrigeration industry regard this problem? (or how did they, rather) For example, when you bought one ton of ice for refrigeration, what were the underlying assumptions about how much cooling that provided? (Now i am thinking of Rocky hefting a block of ice up the New York steps). $\endgroup$
    – Vogon Poet
    Oct 2, 2020 at 20:47

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