4.3 Show that Eq. (4.143) can be written in the form
(sigma(N))/(N)=[(k_B T)/(-(∂P)/(∂(V̂))_T)((N)/(N_A))(V̂)^(2)]^((1)/(2)),
where VÌ‚ is the molar specific volume in (m^(3))/(k)mol.
The relations obtained for a binary system apply to a single-species system if we set N_b to zero and drop μ_b as a parameter. For a single-species system, here we will drop the subscript and designate the number of particles and chemical potential simply as N and μ, respectively. Conversion of relations derived earlier thus requires that we set N_b to zero and replace N_a and μ_a with N and μ respectively. It follows that for a single-species system, the relation for the fractional standard deviation in the number of particles N is given by
(sigma(N))/(N)=[(k_B T)/(-(∂P)/(∂V)_N,T)V^(2)]^((1)/(2))