Response to the following problem:
The equation of state for a monatomic solid is
Pv + f(v) = Γu,
Where v is the molar volume, Γ is the Griineisen constant, and u is the molar internal energy due to lattice vibrations. Prove that
Γ = βu/cvK’
Where K, is the isothermal compressibility. This equation, known as the Griineisen relation, plays an important role in solid-state theory.