# Introduction to Thermodynamics

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## Summary of various disciplines

• Thermodynamics = study of transformation of energy on a macroscopic level (i.e., “large” scale)
• Chemical dynamics (kinetics) = study of the rates and mechanisms of chenical reactions
• Describes how fast things are changing and why
• Quantum mechanics = mathematical description of matter, light, and energy at the microscopic (i.e., atomic/molecular) scale
• Stastistical mechanics = framework for relating propeties of atoms and molecules to thier microscopic behavior

## Applications/Examples of Thermodynamics

Note: These are from the first lecture of Chem 341

• Powering a car
• Which biofuel works best?
• Optimization of chemical reactions
• Calories in food
• Protein folding

## Basic Definitions

Note: These are from the second lecture of Chem 341

System = all materials involved in a process

• Types of systems:
• Isolated systems = cannot exchange energy or matter
• Closed systems = cannot exchange matter (but can exchange energy)
• Open systems = can exchange matter (and energy as well)

Surroundings = the rest of the universe

Examples:

• The Earth: closed system
• Surroundings with respect to the earth:
• Energy input from the Sun
• Energy output into space
• Coffee
• Consider two cases
1. Coffee is contained in a styrofoam cup with a lid
• Aside: the the styrofoam walls are adiabiotic → blocks heat transfer
2. Coffee is contained in a copper cup with a lid
• Aside: the copper walls are diathermal → allows heat transfer
• In both cases, the coffee corresponds to a closed system whose surroundings is everything else in the universe
• However, since the walls in the cooper cups are diathermal, the coffee will cool down more quickly than the coffee in the styrofoam cup

Intensive variables = variables that do not depend on the size of a system (e.g., temperature and pressure)

Extensive variables = variables that depend on the size of a system (e.g., heat and volume)

• Dividing an extensive variable by mass or the number of moles in a system converts it to an intensive variable

Ideal gases = gases comprised of molecules that do not interact or take up space

• Importantly, ideal gases don’t actually exist. They are just useful hypothetical concepts for understanding thermodynamics

Work = any quantity of energy that flows across the boundary between a system and its surroundings

• Work is transitory ⇒ it only exists during processes of change
• SI unit: Joules

Heat = any quantity of energy that flows between a system and its surroundings due to a temperature difference

• Like work, heat is transitory
• Exothermic = heat is transferred into the system
• Endothermic = heat is transferred out of the system

Entropy = not quite a measure of randomness/disorder, but more of a meausre of the number of available states (called configurations) a system has

## Equations

Ideal gas law: $PV = nRT$

• $P =$ pressure (SI units: $1 \mathrm{N} / \mathrm{m^2} = 1 \mathrm{Pa}$ )
• $V =$ volume (SI units: $\mathrm{m^3} = 1 \mathrm{L}$
• $n =$ number of moles
• $R = 1.834 \mathrm{J} / \mathrm{mol} \mathrm{K} =$ ideal gas constant
• $T =$ temperature (SI unit: $\mathrm{K}$)

Van der Waals equation (“real gas law”):

$(P + a \frac{n^2}{V^2})(V - nb) = nRT$

• Variables
• $a$ = strength of interactions between molecules/atoms on a given parameter
• $b$ = size of the molecule/atom
• This is a much more realistic equation for describing basic interactions between molecules
• Accounts for both molecule interactions and the size molecules

## Laws of Thermodynamics

• 0th Law of Thermodynamics = two systems that are separately in thermal equilibrium with a third system are in thermal equilibrium with eachother
• Let $T_i$ be the temperature of system $i$
• If $T_1 = T_3$ and $T_2 = T_3$, then $T_1 = T_2$
• 1st Law of Thermodyamics (Law of Conservation of Energy) = in an isolated system, energy cannot be created or destroyed
• 2nd Law of Thermodynamics = for any spontaneous process to occur, the change in entropy $\nabla S$ must be greater than or equal to zero
• Note: spontaneous chemical reactions can occur that results in a negative change in entropy (as long as there is a sufficient enough change in enthalpy)
• 3rd Law of Thermodynamics = the entropy of a system approaches a constant value as $T \rightarrow 0K$
• Thus, perfectly crystalline solid only has one state at $T = 0K$ ⇒ $S = k \ln{1} = 0$
• This holds if the perfect crystal only has one state with minimum energy
• Allows for calculation of absolute entropies for elements and compounds at any value of $T$

## Sources:

Fall 2014 Chem 341 Lectures (taught by Dr. Joshua Patterson – Chemistry Department at Christopher Newport University)

Physical Chemistry, 3rd Edition, Thomas Engel and Philip Reid Pearson Education Inc. (2013)

https://courses.lumenlearning.com/boundless-chemistry/chapter/the-laws-of-thermodynamics/

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