Thermal expansion coefficient: derivation of relationship between linear expansion and volume expansion

({ alpha }_{ L }) VS ({ alpha }_{ V })

In calculating entropy change for a solid under isothermal pressure change, we used thermal volume expansion coefficient (({ alpha }_{ V })). However, in most cases, not volume but linear expansion coefficients (({ alpha }_{ L })) are available. In the video, we used the relationship

({ alpha }_{ V })=3({ alpha }_{ L })

Here, let’s derive this relationship.