Water Brainteaser

Spring 2003

The stability of liquid water on and within the surface of Mars is key to almost every aspect of martian science. In this exercise we ask you to consider some aspects of the frozen to liquid transition of water within the martian surface.

Heat flow is a key aspect of this problem and many others and, in uniform media, can easily be approximated by the formula:

Q = k . dT/dz
where Q is the heat flow in watts per square meter, K is the conductivity of the material in watts per kelvin per meter and dT/dz is the temperature gradient.

On Mars the heat flow has been guessed by theoretical work to be approximately 30 mW per square meter.

Rearrange the above equation so that you can estimate the depth to the melting temperature of water in terms of a surface temperature.

Assume a conductivity typical of rock (~3 W/m/k) and and global average Martian surface temperature (~200 K). How far down would you expect to find liquid water (assuming there is any water to find).

What about under the polar cap? Typical ice conductivities are 2.25 W/m/k and typical polar surface temperatures are about 160K. The northern polar cap rises about 3Km above the surrounding terrain. Do you think its likely that there is liquid water underneath it? Why ?

What would be the difference if 50% of the polar cap were made up of dirt (rock conductivity). If there were a significant concentration of ionic salts at the base would you expect a significantly different conclusion?

In all these cases we neglect the effect of increased pressure at depth. What effect does increased pressure have on the melting point and how big is that effect (no need for the exact relationship, order of magnitude will do)

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