The thermal expansion coefficient is defined as the fractional increase in the linear dimension of a sample of a substance with increase in temperature at constant pressure. Thus,

For most solids the coefficient β_{p} is positive, typically 10^{−5} and tables are available for many engineering materials Bolz and Ture (1970).

For fluids, it is more usual to work with the volumetric thermal expansion coefficient

which is usually positive and much larger than for solids but is negative for water between 0°C and 4°C.

The volumetric thermal expansion coefficient is readily evaluated if an equation of state is available or, indeed, simply values of the fluid volume as a function of temperature at constant pressure. In the former category, for an ideal gas, it is easily shown that

In the latter category, it is worth noting that

in the thermal expansion coefficient of a liquid at saturation (not constant pressure). However, it is easily shown that the difference between β_{σ} and β_{p} is small while β_{σ} is rather easily determined for measurements of the density of the liquid at saturation. It follows that a good estimate of β_{p} can be obtained from measurements for the saturated liquid density.

#### REFERENCES

Bolz, R. E. and Ture, G. L. (1970) *Handbook of Tables for Applied Engineering Science*, CRC Press, Boca Raton.

Bett, K. E., Rowlinson, J. S. and Saville, G. (1975) *Thermodynamics for Chemical Engineers*, Athlone, London.

#### References

- Bolz, R. E. and Ture, G. L. (1970)
*Handbook of Tables for Applied Engineering Science*, CRC Press, Boca Raton. - Bett, K. E., Rowlinson, J. S. and Saville, G. (1975)
*Thermodynamics for Chemical Engineers*, Athlone, London.