Re: Melting under pressure, was Squeeky Snow.

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

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.

David Bowman
David_Bowman@georgetowncollege.edu