We know that,
du = Tds - Pdv------(i)
dH = du + pdv + vdp-----(ii)
and dG = dH - Tds - sdT------(iii)
Putting the value of dv in equation (ii), we got---
dH = Tds - pdv + pdv + vdp
dH = Tds + vdp------(iv)
Putting the value of dH from equation (iv) to equation (iii), we got
dG = Tds + vdp - Tds - sdT
dG = vdp - sdT
at constant temperature dT = 0
\(\therefore\) dG = vdp, at constant temperature.
