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Vanishing linear term in chemical potential difference in volume term of work of critical nucleus formation for phase transition without volume change

A question is given on the form n(μ_β-μ_α) for the volume term of work of formation of critical nucleus. Here, n is the number of molecule undergone the phase transition, μ denotes the chemical potential, α and β represent the parent and nucleating phases, respectively. In this paper we concentrate phase transition without volume change. We have calculated the volume term in terms of the chemical potential difference μ_{re}-μ_{eq}$ for this case. Here, μ_{re} is the chemical potential of the reservoir and μ_{eq} that at the phase transition. We have W_{vol} = -[(κ_β-κ_α)/(2v_{eq}^2)] (μ_{re}-μ_{eq})^2 V_β with κ denoting the isothermal compressibility, v_{eq} being the molecular volume at the phase transition, V_β the volume of the nucleus.