Replying to Question which came up in class

10. Rank, and give approximate values for, the thermal conductivity of: snow, ice, polyethylene, wood and brass.
- Use thermal conductivity values from Ashby 1989.
- The thermal conductivity for ice, measured at –20 deg C, is 2.4 W/mK [Physics of ice, Petrenko & Whitworth 1999].

Using this data explain why a brass ski would slide less well than a polymer or wood ski.

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Thermal conductivities
snow < ice; snow is about an order of magnitude less than ice, i.e. c. 0.2 W/mK brass c. 100 W/mK
wood c. 0.2 to 0.5 W/mK
polyethylene c. 0.5

When a material slides on ice, or snow (which is ice with pores), heat is generated at the interface by friction. If the thermal conductivities of the materials in contact are similar there will not be preferential heat flow into one or the other (this is the case with polyethylene or wood skis), however for brass the thermal conductivity is significantly higher – so heat is conducted away from the interface into the brass, and is therefore not available at the interface to create melting.

This question was inspired by a classic paper that was the first study to show that skis slide easily on snow because of a layer of lubricating water that occurs because of frictional heating, and not because of pressure melting.
The Mechanism of Sliding on Ice and Snow, F. P. Bowden and T. P. Hughes, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 172, No. 949 (Aug. 3, 1939), pp. 280-298

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