Tds Equations

 Based on the first law of thermodynamics, Heat transfer, Q = Work done (W) + Internal energy (ΔU) TdS = pdV + dU

Tds EQUATIONS

Based on the first law of thermodynamics,

Heat transfer, Q = Work done (W) + Internal energy (ΔU)

TdS = pdV + dU

It can be rewritten as

TdS = dU + pdV     ……(2.33)

For unit mass,

Tds = du + pdv        ….. (2.34)    

Equation (2.33) is the first Tds equation or Gibb's function.

We know that

Enthalpy, h = u + pv

Differentiating above enthalpy equation, it becomes

Enthalpy, dh = du + d(pv) = du + vdp + pdv

⸫ du = dh – vdp – pdv     ... (2.35)

Substituting equation (2.35) in (2.34),

Tds = dh – vdp - pdv + pdv

Tds = dh – vdp    ….(2.36)

Equation (2.36) is the second Tds equation.