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Mathematics for Thermodynamics
Partial Differentiation
The first derivative of a function denotes the change of a function. The second derivative
denotes the change of the first derivative, etc When the function depends only on one
variable, the change
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The Second Law of Thermodynamics
Statements of the 2nd Law of Thermodynamics
Kelvins statement No process is possible in which the sole result is the absorption
of heat from a reservoir and its complete conversion to work.
Picture of heat engine attempt
CHEM 3350 Fall 2009
Exam #1 2 OCT 09
Name_
Show your work for each problem to receive credit. If you are missing some vital information or
need some help, please ask. Please answer each question fully.
1. (20 points) Ideal gases can be defined in terms of
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Phase Transitions
Introduction
Phase substance in a form of matter which is homogeneous throughout both in
chemical composition and physical state.
Transition a change from one state to another at a characteristic temperature and a
given pressure
Accord
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Phase Diagrams
Gibbs Phase Rule
The Gibbs phase rule describes the degrees of freedom available to describe a
particular system with various phases and substances.
To derive the phase rule, let us begin with a system that has c independent chemical
spec
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Chapter Objectives for Thermodynamics
Mathematics
Concepts
Know the distinction between an ordinary derivative and a partial derivative.
Know how to take the partial derivative of a function.
Know how to find the partial derivative of a function using t
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Mixtures and Solutions
Partial Molar Quantities
Partial molar volume
The total volume of a mixture of substances is a function of the amounts of both
substances (among other variables as well). V V ( n1 , n 2 )
Thus the change in volume of a mixture can
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CHEM 3350
Fall 2013
Mathematics Homework Project
1. If u = x 2 ( x 2 + y 2 ) , calculate u x and u y .
2. Calculate dy dz if y = 2sin ( y + z ) .
3. Assume that the reaction rate constant is a function of activation energy and temperature,
k = Ae
EA
RT
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Chemical Kinetics
Chemical kinetics is the study of chemical reactions via their rates. Studying the
concentration dependence of reaction rates gives information about the reaction mechanism.
Reaction Rates
A reaction rate is the speed in which a reacta
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Introduction to Thermodynamics
What is Thermodynamics?
- Thermodynamics is the study of the properties of matter, especially energy.
- Thermodynamics examines the macroscopic properties only
- To examine thermodynamic properties, knowing the details of
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Gases
The Kinetic Theory of Gases
Basics
1. Sample of gas huge number of atoms (molecules).
2. Atoms are very small compared the space in which they travel.
3. Atoms have translational energy only (ignore rotational, vibrational or other
internal struct
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First Law of Thermodynamics
State Functions
- A State Function is a thermodynamic quantity whose value depends only on the
state at the moment, i. e., the temperature, pressure, volume, etc
- The value of a state function is independent of the history o
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Electrolyte Solutions
Review of Electrical Quantities
Charge
Charge is a fundamental is a fundamental characteristic of matter and (similar to mass)
it is understood better for what it does (it attracts and repels) rather than what it is.
Charge is meas
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Electrochemistry
Electrochemical cells
I. Redox reactions
A. involve transfer of electron from one reactant to another reactant to form
products
1. reactant which loses e- is reducing agent (causes reduction)
2. reactant which gains e- is oxidizing agen
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Chemical Equilibrium
Introduction to Chemical Potential
By definition (one of many!) chemical potential, , is
G
n T ,p
However, if G G ( p, T ) , then the derivative with pressure and temperature held
constant must be zero.
The chemical potential is