Linear expansion Linear expansion means change in o ne dimension (length) as opposed to change in volume (volumetric expansion). To a first approximation, the change in length measurements of an object due to thermal expansion is related to temperature change by a "linear expansion coefficient". It is the fractional change in length per degree of temperature change. ssuming negligible effect of pressure, !e may !rite
Volume Volume expansion expans ion #or a solid, !e can ignore the effects of pressure on the material, and the volumetric thermal expansion coefficient can be !ritten
!here
is the volume of the material, and
is the rate of change of that volume !ith temperature.
This means that the volume of a material changes by some fixed fractional amount. #or example, a steel bloc$ !ith a volume of % cubic meter might expand to %.&&' cubic meters !hen the temperature is raised by & . This is an expansion of &.'*. If !e had a bloc$ of steel !ith a volume of ' cubic meters, then under the same conditions, it !ould expand to '.&&+ cubic meters, again an expansion of &.'*. The volumetric expansion coefficient !ould be &.'* for & , or &.&&+* %. If !e already $no! the expansion coefficient, then !e can calculate the change in vol ume
!here
is the fractional change in volume (e.g., &.&&') and
is the change in temperature (& -).
The above example assumes that the expansion coefficient did not change as the temperature changed and the increase in volume is small compared to the original volume. This is n ot al!ays true, but for small changes in temperature, it is a good approximation. If the volumetric expansion coefficient does change appreciably !ith temperature, or the increase in volume is significant, then the above e/uation !ill h ave to be integrated
!here
is the volumetric expansion coefficient as a function of temperature T , and
initial and final temperatures respectively.
,
are the
Thermal expansion Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature, through heat transfer . Temperature is a monotonic function of the average molecular $inetic energy of a substance. 0hen a substance is heated, the $inetic energy of its molecules increases. Thus, the molecules begin moving more and usually maintain a greater average separation. 1aterials !hich contract !ith increasing temperature are unusual this effect is limited in si2e, and only occur !ithin limited temperature ranges (see examples belo!). The degree of expansion divided by the change in temperature is called the material3s coefficient of thermal expansion and generally varies !ith temperature.
Zero Law of thermodynamics The zeroth law of thermodynamics states that if t!o thermodynamic systems are each in thermal e/uilibrium !ith a third, then they are in thermal e/uilibr ium !ith each other. T!o systems are said to be in the relation of thermal e/uilibrium if they are lin$ed by a !all permeable only to heat, and do not change over time. 4%5 s a convenience of language, systems are sometimes also said to be in a relation of thermal e/uilibrium if they are not lin$ed so as to be able to transfer heat to each other, but !ould not do so if they !ere connected by a !all permeable only to heat. Thermal e/uilibrium bet!een t!o systems is a transitive relation. The physical meaning of the la! !as expressed by 1ax!ell in the !ords "ll heat is of the same $ind". 4'5 #or this reason, another statement of the la! is "ll di athermal !alls are e/uivalent". 465 The la! is important for the mathematical formulation of thermodynamics, !hich needs the assertion that the relation of thermal e/uilibrium is an e/uivalence relation. This information is needed for a mathematical definition of temperature that !ill agree !ith the physical existence of valid thermometers.
