Homologous temperature expresses the
thermodynamic temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
of a material as a fraction of the thermodynamic temperature of its
melting point
The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depen ...
(i.e. using the
Kelvin scale
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
):
For example, the homologous temperature of lead at room temperature (25 °C) is approximately 0.50 (T
H = T/T
mp = 298 K/601 K = 0.50).
Significance of the homologous temperature
The homologous temperature of a substance is useful for determining the rate of steady state
creep (diffusion dependent deformation). A higher homologous temperature results in an exponentially higher rate of diffusion dependent deformation.
Additionally, for a given fixed homologous temperature, two materials with different melting points would have similar diffusion-dependent deformation behaviour. For example, solder (T
mp = 456 K) at 115 °C would have comparable mechanical properties to copper (T
mp = 1358 K) at 881 °C, because they would both be at 0.85T
mp despite being at different absolute temperatures.
In electronics applications, where circuits typically operate over a −55 °C to +125 °C range,
eutectic tin-lead (Sn63) solder is working at 0.48T
mp to 0.87T
mp. The upper temperature is high relative to the melting point; from this we can deduce that solder will have limited
mechanical strength
The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the re ...
(as a bulk material) and significant
creep under stress. This is borne out by its comparatively low values for tensile strength, shear strength and modulus of elasticity. Copper, on the other hand, has a much higher melting point, so foils are working at only 0.16T
mp to 0.29T
mp and their properties are little affected by temperature.
References
Scales of temperature
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