# l08 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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20.110/5.60 Fall 2005 Lecture #8 page 1 Fundamental Equations, Equilibrium, Free Energy, Maxwell Relations Fundamental Equations relate functions of state to each other using 1 st and 2 nd Laws 1 st law with expansion work: dU = đ q - p ext dV need to express đ q in terms of state variables because đ q is path dependent Use 2 nd law: đ q rev = TdS For a reversible process p ext = p and đ q = đ q rev =TdS So…… ** dU = TdS – pdV ** This fundamental equation only contains state variables Even though this equation was derived for a reversible process, the equation is always correct and valid for a closed (no mass transfer) system, even in the presence of an irreversible process. This is because U, T, S, p, and V are all functions of state and independent of path. AND The “best” or “natural” variables for U are S and V , ** U(S,V) ** 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field

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20.110/5.60 Fall 2005 Lecture #8 page 2 ** U(S,V) ** From dU = TdS – pdV ** T S U V = ; p V U S = ** We can write similar equations for enthalpy H = U + pV dH = dU + d(pV) = dU + pdV + Vdp inserting dU = TdS – pdV ** dH = TdS + Vdp ** The natural variables for H are then S and p ** H(S,p) ** From dH = TdS + Vdp T S H p = ; V Vp H S = ** _______________ We can use these equations to find how S depends on T. From dU = TdS – pdV T C T U T 1 T S V V V = = From dH = TdS + Vdp T C T H T 1 T S p p p = =
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## This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.

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l08 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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