Deriving the equation for lines of constant enthelpy

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To derive the equation for (dP/dV)H, start with the equation of state, expressing dT in terms of dP and dV. Combine this with the enthalpy equation, dH = C_PdT + (V - T(∂V/∂T)_P)dP. The key is to manipulate these equations while holding enthalpy constant, which may involve using Maxwell relationships and the triple product rule. Despite challenges, these foundational equations provide a pathway to derive the desired expression. A clear understanding of thermodynamic identities is essential for successful derivation.
djkuehlos14
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How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.
 
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djkuehlos14 said:
How would one derive the equation for (dP/dV)H? That is the partial of P over the partial of V, holding H constant. I've tried many different things, triple product rule, maxwell relationships, and nothing seems to work. I appreciate any advice.

You need to start with the equation of state, and write
dT=(\frac{\partial T}{\partial P})_VdP+(\frac{\partial T}{\partial V})_PdV

You need to combine this with the equation:

dH=C_PdT+(V-T(\frac{\partial V}{\partial T})_P)dP
 
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