Show that dg = -sdT + vdp is equivalent to dg = v(dp/dv)dv + (v(dp/dt)-s)dt gibbs...

Show that dg = -sdT + vdp is equivalent to dg = v(dp/dv)dv + (v(dp/dt)-s)dt gibbs energy equation

Expert Solution

Given that dG = -sdt + vdp

dG = vdp - sdt

dG = (dG/dv) dv + (dG/dt) dt

= [(vdp - sdt) /dv]dv + [(vdp - sdt) /dt] dt

= v (dp/dv)dv - s (dt/dv) dv + v (dp/dt)dt - sdt

= v (dp/dv)dv - 0 + v (dp/dt)dt - sdt

= v (dp/dv)dv + v (dp/dt)dt - sdt

= v(dp/dv)dv + [ v(dp/dt)-s] dt

Therefore,

dG = v(dp/dv)dv + [ v(dp/dt)-s] dt

queen_honey_blossom answered 2 years ago

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