ACTIVITY 2-4 . Answer only number 1 This is sometimes called the heat content at constant pressure process, qp .Activity 2-4Let us make use of our knowledge of calculus and derive somethermodynamic relationships from certain functions.1. Internal energy's natural variables are entropy, S, and V.Mathematically, it can be written as U = U(S,V). Write the totaldifferential of U. Derive the Maxwell relation from the totaldifferential and evaluate the partial differentials.2. Read Alberty's publication (Pure Appl. Chem., Vol.73, No. 8, pp.1349-1380, 2001) on Legendre Transforms of U. Generate all theLegendre functions from the relation U = U(S, V, n) of an openone-phase system and the associated Maxwell relations 2.2. The First Law of Thermodynamics [ “YOU CAN’T WIN"]The first law of thermvdynamies relates the change in internal energy asthe system changes state. Internal energy, U, represents the total energy of thesystem which is given as the sum of the kinetie and potential energy of themolecules in the system. Since the absolute value of internal energy cannot bemeasured, only changes in internal energy (AU) are measureable as systems changefrom one state to another state. The change in internal energy is measured atconstant volume processes. Thus it is sometimes referred to as the heat content atconstant volume, q, .The first law is often called as the Law of Conservation of Energy whichstates that energy cannot be created or destroyed; it can only be transformed fromone form into another. The basic energy currency in the first law is heat and work.The mathematical statement of the law isAU = q + wdu = đq + đworwhere q is positive when it is absorbed by the system and negative when heat isreleased into the surrounding. In pressure-volume (PV) work, w is defined asw = - Pop dV, where pop is the opposing or external pressureWork is positive when the surrounding does work on the system; it is negative whenthe system does work on the surrounding. The first law can be stated in this manner- the change in internal energy of the system is equal to the sum of the heat absorbedby the system plus the work done on the system by the surrounding.Vision: The premier untversity of science and technology in the VisayasMission: Provide excellent instruction, conduct relevant research and faster community engagement thatproduce highly competent graduates for the development of the countryPage 40Chem 150 Physical ChemistryLearning ResourceInternal energy, U, is a state function. Changes in its value depends onlyon the internal energies of the final and initial states, e.g., AU = Uánal - Umitial -However, q and w are path functions. Their magnitudes depend on how the changein state is achieved. This entails different ways of solving for the q and w dependingon the change of state processes involved.The change in enthalpy, AH, unlike AU, is measured at constant pressure.This is sometimes ealled the heat content at constant pressure process, qp -

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ACTIVITY 2-4 . Answer only number 1 This is sometimes called the heat content at constant pressure process, qp .Activity 2-4Let us make use of our knowledge of calculus and derive somethermodynamic relationships from certain functions.1. Internal energy's natural variables are entropy, S, and V.Mathematically, it can be written as U = U(S,V). Write the totaldifferential of U. Derive the Maxwell relation from the totaldifferential and evaluate the partial differentials.2. Read Alberty's publication (Pure Appl. Chem., Vol.73, No. 8, pp.1349-1380, 2001) on Legendre Transforms of U. Generate all theLegendre functions from the relation U = U(S, V, n) of an openone-phase system and the associated Maxwell relations 2.2. The First Law of Thermodynamics [ “YOU CAN’T WIN&#34;]The first law of thermvdynamies relates the change in internal energy asthe system changes state. Internal energy, U, represents the total energy of thesystem which is given as the sum of the kinetie and potential energy of themolecules in the system. Since the absolute value of internal energy cannot bemeasured, only changes in internal energy (AU) are measureable as systems changefrom one state to another state. The change in internal energy is measured atconstant volume processes. Thus it is sometimes referred to as the heat content atconstant volume, q, .The first law is often called as the Law of Conservation of Energy whichstates that energy cannot be created or destroyed; it can only be transformed fromone form into another. The basic energy currency in the first law is heat and work.The mathematical statement of the law isAU = q + wdu = đq + đworwhere q is positive when it is absorbed by the system and negative when heat isreleased into the surrounding. In pressure-volume (PV) work, w is defined asw = - Pop dV, where pop is the opposing or external pressureWork is positive when the surrounding does work on the system; it is negative whenthe system does work on the surrounding. The first law can be stated in this manner- the change in internal energy of the system is equal to the sum of the heat absorbedby the system plus the work done on the system by the surrounding.Vision: The premier untversity of science and technology in the VisayasMission: Provide excellent instruction, conduct relevant research and faster community engagement thatproduce highly competent graduates for the development of the countryPage 40Chem 150 Physical ChemistryLearning ResourceInternal energy, U, is a state function. Changes in its value depends onlyon the internal energies of the final and initial states, e.g., AU = Uánal - Umitial -However, q and w are path functions. Their magnitudes depend on how the changein state is achieved. This entails different ways of solving for the q and w dependingon the change of state processes involved.The change in enthalpy, AH, unlike AU, is measured at constant pressure.This is sometimes ealled the heat content at constant pressure process, qp -

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1. Internal energy's natural variables are entropy, S, and V. Mathematically, it can be written as U=U(S,V). Write the total differential of U. Derive the Maxwell relation from the total differential and evaluate the partial differentials.