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 p ...

T_H = \frac

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

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(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

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(as a bulk material) and significant

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 {{Measurement-stub