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Derive the energy equation for a van der Waal gas.
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[QUOTE="Chestermiller, post: 4696850, member: 345636"] [tex]dU=TdS-PdV=T\left(\frac{∂S}{∂T}\right)dT+T\left(\frac{∂S}{∂V}\right)dV-PdV= C_VdT+(T\left(\frac{∂S}{∂V}\right)-P)dV[/tex] The next step is to determine ∂S/∂V at constant T. This can be obtained from a Maxwell relation, starting from the equation dA=-SdT-PdV. S=-∂A/∂T P=-∂A/∂V So [tex]\frac{∂S}{∂V}=\frac{∂P}{∂T}[/tex] Therefore, [tex]dU=C_VdT+(T\left(\frac{∂P}{∂T}\right)-P)dV[/tex] The second term in this equation is zero for an ideal gas, but not for a real gas. Just substitute the van der Waals equation into the second term of this equation. chet [/QUOTE]
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Derive the energy equation for a van der Waal gas.
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