Back to Table of Contents [TOP]  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 non-expansion work we have: Therefore we may re-write 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 p-V 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: NOTE: The full set of the Maxwell relationships may be derived form the other thermodynamic functions and are summarised as follows (not examinable):

 CH237 - Chemical Thermodynamics and Kinetics

 BACK TO TABLE OF CONTENTS   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 non-expansion work we have: Therefore we may re-write 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 p-V 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: NOTE: The full set of the Maxwell relationships may be derived form the other thermodynamic functions and are summarised as follows (not examinable):

[ UNIVERSITY OF MALTA | FACULTY OF SCIENCE | DEPARTMENT OF CHEMISTRY ]

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