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Combining the first and second laws of thermodynamics  The fundamental equations of thermodynamics (1) The fundamental equations of thermodynamics The first law of thermodynamics may be written as: where for a reversible change a closed system of constant composition, and in the absence of nonexpansion work we have:Therefore we may rewrite the first law as: THIS REALTIONSHIP IS KNOWN AS THE FUNDAMENTAL EQUATION OF THERMODYNAMICS . We will revisit this equation at a later stage to include the effects of changing the composition of the system (the fundumental equation of chemical thermodynamics.)This equation shows how the internal energy of a closed system changes with changes in S and V, i.e. U = U(S,V). Now, because dU is an exact differential (U is a state function), its value is path independent, i.e. this equation is valid for all types of processes of a closed system that does no non pV work. (2) Use of the Fundamental Equation to generate new functions (Derivations not examinable.) If we where to differentiate U = U(S,V) we get: i.e. from the fundamental equation we see that: and Another very interesting equation (one of a set called the Maxwell relationships) may be obtained from the property that if for U = U(x,y) , dU is an exact differential, then we have: which in our case we have: i.e.: or:


CH237  Chemical Thermodynamics
and Kinetics
Dr.
Joseph N. Grima, Department
of Chemistry

Combining the first and second laws of thermodynamics  The fundamental equations of thermodynamics (1) The fundamental equations of thermodynamics The first law of thermodynamics may be written as: where for a reversible change a closed system of constant composition, and in the absence of nonexpansion work we have:Therefore we may rewrite the first law as: THIS REALTIONSHIP IS KNOWN AS THE FUNDAMENTAL EQUATION OF THERMODYNAMICS . It shows how the internal energy of a closed system changes with changes in S and V, i.e. U = U(S,V). Now, because dU is an exact differential (U is a state function), its value is path independent, i.e. this equation is valid for all types of processes of a closed system that does no non pV work. (2) Use of the Fundamental Equation to generate new functions If we where to differentiate U = U(S,V) we get: i.e. from the fundamental equation we see that: and Another very interesting equation (one of a set called the Maxwell relationships) may be obtained from the property that if for U = U(x,y) , dU is an exact differential, then we have: which in our case we have: i.e.: or:

Email me at jgri1@um.edu.mt 