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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

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,...)

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) (j3,4,5,,n)
- This holds for mixtures as well, but composition

must also be defined - Ij f(I1, I2, x1,x2,,xm-1) (j3,4,5,,n)
- for an m-component mixture.

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) (j3,4,5,,n

) - for an m-component mixture.
- The quotient Ei / m (molar volume, molar Gibbs

energy) is an intensive variable, often called a

specific property

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)

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?

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 (AB),

we find - dQ lt TdnS AND dW lt 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.

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

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.

3. Defining Maxwells Equations

- Purpose of this lecture
- Introduction into the Maxwells equations
- Learning objectives
- To understand and apply the criterion of

exactness to fundamental property relations - To understand where and how Maxwells relations

are useful - To achieve competence in deriving and applying

the Maxwells equations toward the calculation of

thermodynamic property changes - Reading assignment Chapter 6.1 from the textbook

Defining Maxwells Equations

- The fundamental equations can be expressed as
- from which the following relationships are

derived

Maxwells 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 Maxwells relations - 6.13-6.16

Maxwells Equations - Example 1

- We can immediately apply Maxwells 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 HH(T,P)
- The final expression, including the pressure

dependence is - 6.20
- Which for an ideal gas reduces to
- 6.23

Maxwells Equations - Example 2

- Entropy Dependence on T,P-closed system
- Given that SS(T,P)
- The final expression, including the pressure

dependence is - 6.21
- Which for an ideal gas reduces to
- 6.24

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)

Answers (a)

(b)

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