Really appreciate if someone could at least direct me in the rightdirection. Tha

Question

Really appreciate if someone could at least direct me in the rightdirection. Thanks!

Explanation / Answer

dU = T*dS - P*dV dS = (dS/dT)V*dT + (dS/dV)T*dV From dF = -S*dT - P*dV,      (dS/dV)T =(dP/dT)V       (MaxwellRelation) dS = (dS/dT)V*dT + (dP/dT)V*dV Sub into dU = T*dS - P*dV dU = T*[(dS/dT)V*dT + (dP/dT)V*dV] - P*dV dU = T*(dS/dT)V*dT + [T*(dP/dT)V - P] dV dS/dT = Cv/T   =>    dU = Cv*dT +[T*(dP/dT)V - P] dV     [T*(dP/dT)V - P] is the internal pressure P = RT/(V-b) - a/V2 => (dP/dT)V = R/(V-b) So dU = Cv*dT + [T*R/(V-b) - P] dV     T*R/(V-b) - P = T*R/(V-b) - [RT/(V-b) - a/V2] =a/V2    b - (V-b)*x/(1-x) = b -2a(V-b)3/RTV3/ [ 1 -2a(V-b)2/RTV3] Note (V-b)2/V3 => 0   and(V-b)3/V3 => 1 b - (V-b)*x/(1-x) ~ b - 2a/RT / ( 1 - 0) ~ b - 2a/RT = -(dH/dP)T / Cp = -[V - T*dV/dT|P]/Cp = -( b - 2a/RT)/Cp = (2a/RT - b)/Cp See here for more

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