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Concerning Ludwik's comment:
The "melting under pressure" idea was discussed here several
winters ago. It was pointed out that pressure must be very
high to produce melting. I do not think that pressures
generated by shoes are sufficiently large.
I don't off-hand remember the discussion, but let's just check the
numbers anyway. If we assume the usual quoted numbers of:
(a) liquid water having a density that is 9 % greater than ice, (b) the
normal melting point of water being 273.15 K, and (c) the latent heat of
fusion of water having the value of 333 kJ/kg (i.e. 80 cal/g) we can use
the Clausius-Clapyron equation to determine the melting point depression
with increasing pressure. The value that I get is that the melting point
decreases with increasing pressure at rate of 7.5 mK/atm. If we take
this number at face value we see that to produce a depression of only
5 deg C in the melting point we need to exert a pressure of nearly
670 atm. For some reason I don't think even very obese humans with tiny
feet can exert such pressures between their shoes and the ice/snow
covered ground by walking. So it appears that Ludwik is on solid ground
(rather than on thin ice, or rather than being all wet) with his above
claim.