On the vacation sheet problem, this is how I did it: (I'm not sure if it's correct, but I'll have a tute on it with blundell, I suspect, so I'll ask the best way)
Along the line of co-existence, the gibbs functions have to be identical:
g_1(p,T) = g_2(p, t) => dg_1(p,T) = dg_2(p,T)
dg_1 = -S_1dT + v_1dp = dg_2 = -S_2dT + v_2dp
say 1 is liquid, 2 is gas. v_2 >> v_1 therefore we can ignore the v_1 term.
dp/dT = (s_2 -s_1)/v_2 = delta(s)/v_2
Latent heat = Tdelta(s)
=> dp/dT = L/TV (change v_2 -> V for simplicity of notation)
V = p/RT for one mole
dp/p = (L/R) dT/T^2
integrate all up => p=p_0exp(-L/RT)
L = 2.26E6 J/Kg
We know at STP, water will boil at 100 C. Therefore, all you need to do then is to substitute values in for the mountaintop at hawaii and find the temp needed. If it is less than 97, you're laughing.
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Sorry, forgot to mention: Naturally, my answer depends on knowing the latent heat of vapourisation of water. If you don't have that as assumed knowledge, then I don't know how to answer it; you have too many constants and not enough information.