Thermodynamics Fundamentals

CHEM 205 Physical Chemistry

• This course covers thermodynamics, spectroscopy, and kinetics.

Part I. Thermodynamics

• Concerned the study of transformations of energy.
• Thermodynamics is central to chemistry, biological processes, and thus life.
• Thermodynamics explains why reactions occur, reactions' driving forces, and energy a reaction generates or requires.

Introduction: The Properties of Gases

• Gases serve as the working substance in many machines, e.g., heat engines and refrigerators, and it is important to understand their properties.
• Gas phase is the simplest state of matter to treat theoretically, and it shows universal limiting behavior.
• Development of thermodynamic concepts will largely deal with the gas phase because of its simplicity and generality.

State, State Function, Equation of State

• System state is defined by properties, which are also referred to as state functions (e.g., p, V, T, and n).
• State functions' values describe the system state and can be related by an algebraic expression also known as an equation of state

Ideal Gas Equation of State: "Ideal Gas Law"

• For ideal gases at a low pressure, the state equation is pV = nRT or pVₘ = RT

• p represents pressure in Torr or mmHg.

• V represents volume.

• Vₘ equals V/n and is molar volume.

• n represents the number of moles.

• R is the ideal gas constant: 8.314 J K⁻¹ mol⁻¹, 0.082 L atm K⁻¹ mol⁻¹, 0.08314 L bar K⁻¹ mol⁻¹, 8.314 L kPa K⁻¹ mol⁻¹, or 62.36 L Torr K⁻¹ mol⁻¹.

• T represents temperature.

• K = °C + 273.15

• Pressure units include pascal (Pa), where 1 Pa = 1 kg·m⁻¹·s⁻² = 1 N·m⁻², and conventional units like bar, atm, and Torr.

• 1 bar equals 10⁵ Pa or 100 kPa.

• 1 atm equals 1.01325 × 10⁵ Pa or 101.325 kPa, and 760 Torr.

• 1 Torr (1 mmHg) is 133.322 Pa.

• 1 atm is 14.7 lb·in.⁻² (psi).

Procedures for using the ideal gas law:

• Rearrange pV = nRT to give the desired quantity on the left and all other quantities on the right.
• Convert data to SI units with T in Kelvins.
• Substitute data into the equation with R = 8.314 J K⁻¹ mol⁻¹.

Kinetic Model of Gases, Internal Energy and Temperature

• The kinetic model of gases provides a molecular interpretation of the ideal gas law and leads to a relation between internal energy and temperature.

Assumptions for perfect gas:

• A gas consists of molecules in random motion.

• Gas molecules are infinitesimally small points.

• The molecules move in straight lines until they collide.

• The molecules do not interact, except during collisions.

• All collisions are elastic.

• Ideal gas exerts pressure due to collisions.

• Pressure equals (Δ momentum / area) × (1 / Δt) or force / area.

• Amomentum equals 2mvₓ.

• Simplified Derivation with box size x = y = z = 1, and Box Volume: V = 111 = [3

• Since all directions are equivalent: (vₓ²) = (vᵧ²) = (v₂²) = (v²) / 3.

• Nm (v²) = PV or Mean square velocity: (v²) = (v₁² + v₂² + ... + vₙ²) / N

• PV = Nm (v²) / 3

• For one mol, P = N of N₁m (v²) = 3RT. (Nₐ is Avogadro's number which is equivalent 6.022 × 10^23 mol⁻¹)

• Average translational kinetic energy of one mole of ideal gas: Eₜrans = Nₐ × (½) m (v²) = (3/2) RT or R T/2 to Eₜrans kB equals Boltzmann's constant or R/Nₐ.

• etrans = (3/2)kBT, where kB = R/Nₐ is Boltzmann's constant.

• For an ideal gas (PV=nRT), the internal energy U, which is pure kinetic energy, which is a function of T only.

• At high temperatures, the Equipartition Principle dictates each translational degree of freedom contributes RT/2 to the translational energy.

• Each rotational degree of freedom also contributes RT/2.

• Each vibrational degree of freedom contributes RT to the total internal energy.

• Rigid diatomic molecules have U = (7/2)RT at high temperature because there are 3 translational, 2 rotational, and 1 vibrational degrees of freedom.

• At room temperature, the high-temperature limit is only usually reached for translation and rotation, but not for vibration. The the internal energy is U = (5/2)RT, without the vibrational RT.

• For normal temperatures (around 300K) when statisitcal mechanics are applied:

• Uₜᵣₐₙₛ = (3/2) nRT

• Uᵣₒₜ = (3/2) nRT for non linear and nRT for linear molecules

• Uᵥᵢᵦ approximately equal to 0 for small diatomic molecules

• According to Equal Partition principle, for an ideal gas, U = (3/2)nRT.

• For linear molecules, otherwise ideal behavior, U = (5/2)nRT

• For no-linear molecules, otherwise ideal behavior, U = 3nRT.

• Internal energy U of an ideal gas depends only on T or U equals U(T).

• In real gases, the finite size of the molecules and their interactions lead to deviations from the ideal gas law.

• Internal energy is no longer a function of temperature and pressure equal U(T,V).

Real Gas, Van der Waals Equation

• Repulsive interactions between molecules prevent closer approach than a certain distance and Actual volume in which the molecules can move is thus reduced.

• Therefore, the V in the ideal gas law is replaced by (V - nb), where b is the volume/mole "occupied" by the gas itself.

• Attractive forces that acts on one molecule is proportional to the gas density n/V and the resulting change in the pressure is proportional to (n/V)². , reducing the observed pressure.

• Pideal in the ideal gas law is replaced by (p + an²/V²). Therefore (p + an²/V²) (V-nb) = nRT

• Compressibility factor is z = pV/ (nRT). For an ideal gas: z equals 1.

General Virial equation:

z= (pV / nRT =) =1+ (B₂p / RT) • p+ (B₃p/RT) •p² + (B4p/RT) •p³ +... where B₂p, B₃p, B4p are Virial coefficients. At moderate pressures, z equals (pV /nRT) = 1 + (B₂p/RT)•p

Laws of Thermodynamics

• The laws of thermodynamics deal with the study of transformation of energy, which includes chemical reactions' energy output, reaction direction, and equilibrium conditions.

• The zeroth law defines the temperature.

• The first law is a formulation of the conservation of energy.

• The second law tells us in which direction a process or chemical reaction proceeds spontaneously.

• The third law defines the absolute entropy.

• System is part of the universe of interest.

• Surroundings are the rest.

• Universe is System plus Surroundings.

• Boundary is interface between the system and the surroundings.

• Properties of a system are state functions such as mass, number, volume, temperature, and pressure.

• Equation of state is set of state functions describing system related by algabraic expressopn, e.g., pV=nRT

• Open systems exchange both energy and matter with surroundings.

• Closed system can exchange energy but not matter.

• Isolated system can exchange neither energy nor matter.

Zeroth Law and First Law

• Zeroth Law of Thermodynamics: Two systems in thermal equilibrium with a third one are also in thermal equilibrium with each other.

• The systems are related by the same temperature T, thus the zeroth law defines the temperature and 0 °C = 273.15 K ≈ 273 K.

• First Law of Thermodynamics: Energy can neither be created nor destroyed, although it can be converted from one form into another.

• The state function internal energy U which is the sum of all forms of energy in the system with a constant U = constant for an isolated system.

• Internal Energy SI unit is in Joules (J). , Molar Internal Energy: Um = U/n with SI unit: J/mol, & U = E in Chem 205. For a closed system, the first law is expressed as: AU equals U final - Uinitial and that equals q + w

• infinitesimal change: dU = dq + dw.

• The delta U is the change in internal energy of the system & dU is infinitesimal change in internal energy Note: U is a state function and it is NOT path dependent, dU is used for infinitesimal change. q and w are NOT state functions and are path dependent, δq & δw should be used for infinitesimal change.

• First law of themodynamics: Energy cannot be created or destroyed. ∆U = q + w for a closed system. If U final - Uinitial is the change in Internal Energy: then q positive is the Heat flow into the system & qu negative is the Heat flow out of the system. If is the work done ON the system and, w negative Work done BY the system. q=Δq & w=Δw is the thermodyamics convention

• State function is a property characteristic of the system and it independent of the system history. , P, V, m, T, and U are state functions along side H, G, and S where as q and w are not state functions

• A state function is a physical property dependent on the present state of the system while also being indepent of how the state was prepaired, like density, internal energy U, pressure p, volume V, temperature T, etc

• Processes by which a system can change include irreversible and reversible.

IRREVERSIBLE Processes:

• System is not always in equilibrium.
• Cannot be reversed by an infinitesimal change of its properties.
• Cycle ends returning the system to initial states whilst the surroundings have experienced a permanent change.
• Spontaneous processes have a predetermined direction but are irreversable like, life or breaking eggs

REVERSIBLE Process:

• System is always in equilibrium.
• Cycle ends returning the system to initial states whilst the surroundings have not experienced a permanent change.
• Also referred as Quasi-static.
• Direction is not predetermined.

Isothermal Process: A constant temperature process may be necessary for the surroundings to act as a heat reservoir so that the system boundary must permit heat flow. Isobaric Process: A constant pressure process. Isochoric Process: A constant volume process. Adiabatic Process: A process in which no heat enters or leaves the system. Exothermic Process: A process where heat released into the surroundings as a result the loses energy. Endothermic Process: This absorbs heat from the surroundings resulting in the gains of energy.

• Energy can be exchanged between in a closed system and its surroundings via Heat or Work.

• Heat is the amount of heat transferred between the system and the surroundings: SI unit J (Joules). Sq stands for amount of infinitesimal heat: if heat that are added to the system from the surroundings its called endothermic and Q>0.

• if the system release heat to the surroundings also know as exothermic then Q<0

• Work is the amount of work between the system and the surroundings where its Stand unit is in Joules and dW stands for infinitesimal work.

• If the surroundings do work on the system its referred to as +energy with +w , and if the system does work on the surrounding and its - energy with -w.

Calculation of Expansion Work: where Pex external pressure exerted on the gas, NOT internal gas pressure; final |: where "we=-pex [dv In general |: where W: initial Free Expansion: where =0, then means AU and =0

• There are two different paths between the same initial state and final states as the system.

Different Paths

• In reversible: gas does expand isothermally meaning the heat as the gas expand the energy losed as flow needs work to be re stored.

-In reversible: Gas expand is thermically meaning no work exist. to vacuum.

• Expansion is the Compression with constant.

Enthalpy:

• PV as well as energy units can defines U + PV
• Delta H can also define U2 + P2V2 & U1+P1V1 where it state function
• PV-N: M2: N:Joule
• At constant volume: du & Qy Δυ
• At constant volume AH equals Qp.

Measurement:

Calibration process measurement of hear and Q: CAT. Where C heat of capital of calori meter. Calorimeter: heat absorbed over temperature change.

Heat Capacity CV Cp CVm Cpm & cps and defined = dQ/dT cр = (H ) Cv = ()

For P = constant - Heat exchange at calori change = H For.V = Constant: Heat exchange at const vol = CV The two Cases

Volume in V - constant, - U = Q = n : Cym * dT

At constant B/s is defined as Althy B the allow us to kee[ Track of heat charge at constant pressure as it also defined as:H: U + pV Molar :hm+ H/n; [h]=j/M

(a) at constant p H" - A" at A" as u40 U1+ PV

Heat releases and absorbs energy during enthalpy. Equal enthalpy

Def of hear change capacity- @ constant pressure " & /AT = M * cpm - [ 3 ] + [ * ] - Heat capacity (J/K). [j.k-mol)] ΔH:qP

• ( for P = constant, M const A".QP Cpmm (47)=4H (47) - DH "7m or AH = Qs (p^0 = a* = m comdT

@ " allows us to keep track of hear change Q+ const oressure" (p" + p) H1 +Q • CV/T, M == A and D4 A

Relationship in CV in and 4 pin for ideal cases: A= U + pV"U + nFT -- CH = dv + FRT"DH+ din 2 H" dv DH 41m - AT - dT- &T 4R- V" A+F ""43 " ""+ R + R == C +B

Q" C + D ==End of summary for "CHEM 205 Physical Chemistry"==

Explore the principles of thermodynamics, including energy transformations and the ideal gas law. Learn about state functions, the ideal gas constant, and the behavior of gases. Understand the laws of thermodynamics and their applications in closed and isolated systems.