1. Thermodynamic Systems: Definitions

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1. Thermodynamic Systems: Definitions. Purpose of this lecture : To refresh your memory about some major concepts, definitions, and thermodynamic property relations that we will be using in CHEE 311 Learning objectives To be able to distinguish between isolated, closed, and open systems

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1. Thermodynamic Systems: Definitions
• Purpose of this lecture:
• To refresh your memory about some major concepts, definitions, and thermodynamic property relations that we will be using in CHEE 311
• Learning objectives
• To be able to distinguish between isolated, closed, and open systems
• To understand the definition of intensive and extensive variables
• How the fundamental equation for closed systems is being derived from the 1st and 2nd Laws of Thermodynamics
• To be able to derive the property relations for H, G, A
• Reading assignment: Chapter 6.1 from the textbook

Thermo I Review –Key Concepts

Thermodynamic Systems: Definitions
• The first step in all problems in thermodynamics is to define a system, either a body or a defined region of space.
• Types of Systems:
• Isolated: no transfer of energy or matter across the system boundaries
• Closed: possible energy exchange with the environment but no transfer of matter
• Open: exchange of energy and matter with the environment
• Phase: part of a system that is spatially uniform in its properties (density, composition,...)

Thermo I Review –Key Concepts

Thermodynamic Properties
• Thermodynamics is concerned with macroscopic properties of a body, not atomic properties
• Volume, surface tension, viscosity, etc
• Divided into two classes
• Intensive Properties: (density, pressure,…)
• specified at each point in the system
• spatially uniform at equilibrium
• Usually, specifying any 2 intensive variables defines the values of all other intensive variables

Ij = f(I1, I2) (j=3,4,5,…,n)

• This holds for mixtures as well, but composition must also be defined

Ij = f(I1, I2, x1,x2,…,xm-1) (j=3,4,5,…,n)

for an m-component mixture.

Thermo I Review –Key Concepts

Thermodynamic Properties
• Extensive Properties: (volume, internal energy,...)
• Additive properties, in that the system property is the sum of the values of the constituent parts
• Usually, specifying any 2 intensive and one extensive (conveniently the system mass) defines the values of all other extensive variables

Ej = m * f(I1, I2, x1,x2,…,xm-1) (j=3,4,5,…,n)

for an m-component mixture.

• The quotient Ei / m (molar volume, molar Gibbs energy) is an intensive variable, often called a specific property

Thermo I Review –Key Concepts

2. The Fundamental Equation
• Closed Systems
• We require numerical values for thermodynamic properties to calculate heat and work (and later composition) effects
• Combining the 1st and 2nd Laws leads to a fundamental equation relating measurable quantities (PVT, Cp, etc) to thermodynamic properties (U,S)
• Consider n moles of a fluid in a closed system
• If we carry out a given process, how do the system properties change?
• 1st law:
• dnU = dQ + dW
• when a reversible volume change against an external pressure is the only form of work

dWrev = - P dnV (1.2)

Thermo I Review –Key Concepts

The Fundamental Equation
• When a process is conducted reversibly, the 2nd law gives:

dQrev = T dnS (5.12)

• Therefore, for a reversible process wherein only PV work is expended,
• dnU = T dnS - P dnV (6.1)
• This is the fundamental equation for a closed system
• must be satisfied for any change a closed system undergoes as it shifts from one equilibrium state to another
• defined on the basis of a reversible process, does it apply to irreversible (real-world) processes?

Thermo I Review –Key Concepts

Fundamental Eqn and Irreversible Processes
• The fundamental equation:
• dnU = T dnS - P dnV
• applies to closed systems shifting from one equilibrium state to another, irrespective of path.
• Note that the terms TdnS and PdnV can be identified with the heat absorbed and work expended only for the reversible path.
• dQ + dW = dnU = TdnS - PdnV
• whenever we have an irreversible process (A®B), we find

dQ < TdnS AND dW < PdnV

• the sum yields the expected change of dnU
• Given our focus on fluid phase equilibrium, the lost ability to interpret the meaning of TdnS and PdnV is of secondary importance.

Thermo I Review –Key Concepts

Auxiliary Functions
• The whole of the physical knowledge of thermodynamics (for closed systems) is embodied in P,V,T,U,S as related by the fundamental equation, 6.1
• IT IS ONLY A MATTER OF CONVENIENCE that we define auxiliary functions of these primary thermodynamic properties.
• Enthalpy: H º U + PV 2.11
• Helmholtz Energy: A º U - TS 6.2
• Gibbs Energy: G º H - TS 6.3
• = U + PV - TS
• All of these quantities are combinations of previous functions of state and are therefore state functions as well.
• Their utility depends on the particular system and process under investigation

Thermo I Review –Key Concepts

Differential Expressions for Auxiliary Properties
• The auxiliary equations, when differentiated, generate more useful property relationships:
• dnU = TdnS - PdnV = U(S,V)
• dnH = TdnS +nVdP = H(S,P)
• dnA = -PdnV - nSdT = A(V,T)
• dnG = nVdP - nSdT = G(P,T) (6.7-6.10)
• Given that pressure and temperature are process factors under our control, Gibbs energy is particularly well suited to fluid phase equilibrium design problems.

Thermo I Review –Key Concepts

3. Defining Maxwell’s Equations
• Purpose of this lecture:
• Introduction into the Maxwell’s equations
• Learning objectives
• To understand and apply the criterion of exactness to fundamental property relations
• To understand where and how Maxwell’s relations are useful
• To achieve competence in deriving and applying the Maxwell’s equations toward the calculation of thermodynamic property changes
• Reading assignment: Chapter 6.1 from the textbook

Thermo I Review –Key Concepts

Defining Maxwell’s Equations
• The fundamental equations can be expressed as:
• from which the following relationships are derived:

Thermo I Review –Key Concepts

Maxwell’s Equations
• The fundamental property relations are exact differentials, meaning that for:
• defined as:
• 6.11
• then we have,
• 6.12
• When applied to equations 6.7-6.10 for molar properties, we derive Maxwell’s relations:
• 6.13-6.16

Thermo I Review –Key Concepts

Maxwell’s Equations - Example #1
• We can immediately apply Maxwell’s relations to derive quantities that we require in later lectures. These are the influence of T and P on enthalpy and entropy.
• Enthalpy Dependence on T,P-closed system
• Given that H=H(T,P):
• The final expression, including the pressure dependence is:
• 6.20
• Which for an ideal gas reduces to:
• 6.23

Thermo I Review –Key Concepts

Maxwell’s Equations - Example #2
• Entropy Dependence on T,P-closed system
• Given that S=S(T,P)
• The final expression, including the pressure dependence is:
• 6.21
• Which for an ideal gas reduces to:
• 6.24

Thermo I Review –Key Concepts

Example #3

SVNA 6.21 - The state of 1(lbm) of steam is changed from saturated vapour at 20 psia to superheated vapour at 50 psia and 1000F. (a) What are the enthalpy and entropy changes of the steam?

(b) What would the enthalpy and entropy changes be if steam were an ideal gas?

Properties from Steam Tables (SVNA):