Do all solids have a melting point? For example, is there a point when a tree, a piece of paper, or other carbon based solid becomes a liquid?
No in the sense that a material must maintain an identical chemical makeup and then change from one phase to another, not all solids have a melting point.
Many materials, for example paper, will begin having chemical reactions with surrounding materials as temperature increases, before a phase change, as paper will burst into flame (by combining with atmospheric oxygen) at about 450 degrees F. Even in a vacuum, many materials will begin chemical decomposition before they can change phase. I would expect a complex mixture of large organic molecules like wood to undergo various catabolic reactions as first macromolecules and then smaller molecules gained enough activation energy to break down into simpler, less energetic (i.e. lower enthalpy) constituents, long before these molecules were able to change phase.
Rob Landolfi, Science Teacher, Washington, DC
All common solids will typically go through one of three types of transformations when heated:
Changing from a solid to a liquid state such as when a metal, wax or ice is heated to its melting point, or the specific temperature at which melting occurs.
Changing directly from a solid to a gas in a process known as sublimation. An example of sublimation occurs with dry ice (frozen carbon dioxide) when it is exposed to room temperature, or sulphur when it is heated gradually without being ignited.
Decomposition, which is a breaking apart of the chemicals in the material being heated. Decomposition occurs in many common organic mixtures and compounds such as foods, wood or paper. These materials usually do not melt or liquefy in a visible way, although some of the resulting chemicals or decomposition products do melt and mix with the remaining carbonaceous mass. If the decomposed mass is heated further, there is a temperature at which all the chemicals present will either melt or sublime.
There are conditions under which some materials can either be caused to sublime instead of melting, or liquefy instead of subliming. Common examples are the sublimation of ice under a vacuum during freeze drying, or the liquefaction (melting) of sulphur under high pressure.
The presence of oxygen will have a dramatic effect on the heating of organic materials. When heated in air, most plant or animal substances will partially decompose and then ignite and be converted to combustion products ' mostly water and carbon dioxide. The ashes that remain are a mixture of salts and oxides that will melt at high temperatures.
Scott Wilber, President, ComScire - Quantum World Corporation
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'