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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 = βv/cvk'

Where K, is the isothermal compressibility. This equation, known as the Griineisen relation, plays an important role in solid-state theory.

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