Thermal Expansion and Heat Transfer

Thermal Expansion

A rod of length L will expand by L when its temperature increases by T. It is found L is proportional to T,

L = LT,

where is the one dimensional thermal expansion coefficient. These coefficients appear in tables and vary depending on the material. Thermal expansion is important in engineering applications--- even electrical engineers have to be aware of this phenomenon in the design of microcircuits.

Heat Transfer

Heat transfer falls under the category of redundant phrases. But it is part of the language, so we continue to use it.

There are three modes of heat transfer.

Conduction

In this case, the energy transfer takes place between two points of an object (e.g. a solid) that are held at different temperatures.

More specifically, say we have a solid cylinder of length L and cross-sectional area, A. If one end of the rod (x=0) is held at a high temperature, TH, and the other end of the rod (x=L) is held at a low temperature, TC, then energy will flow from x=0 toward x=L. The power transmitted in Watts we write as,

H dQ/dt (thermal power or thermal current)

The law of heat conduction states,

H = -kA dT/dx ,

where k is called the thermal conductivity of the material, dT/dx is called the temperature gradient. The minus sign is present to assure energy flows from hot to cold.

The above takes on a simpler form for the case of our cylinder,

H = -kA {TC – TH}/L .

A table of k values is in your textbook—metals generally have large k values, while styrofoam a low value.

Convection

Convection is energy transfer by the movement of a hot fluid. It is difficult (but not impossible) to model convection with a simple expression, so just be aware of what it is. Convection is very important in the weather where massive thermal currents develop.

Radiation

Radiation transfers energy because electromagnetic radiation waves are made of energy, for example, sunlight.

Ultimately radiation arises from the acceleration of electric charge, now you know how to create light. The law of radiation states, H = e A T4 [Stefan-Boltzmann Law]

e = emissivity (dimensionless fraction) = Stefan-Boltzmann universal constant A = surface area of emitting body T = absolute temperature of emitting body.

EXAMPLES [in class]