Thermodynamics: Laws, Processes & Entropy

Basic Concepts and First Law

• An open system exchanges both energy and matter with its surroundings
• Internal energy of an ideal gas relies on its temperature
• Enthalpy is a state function
• In an isothermal process with an ideal gas, internal energy remains constant
• Adiabatic processes involve no heat transfer
• First law of thermodynamics states energy conservation

Thermodynamics Calculations

• 2.5 moles of an ideal gas at 300 K absorb 5.0 kJ heat at constant volume with a molar heat capacity of 20.8 J/(mol·K); the final temperature of the gas is 396 K

Heat Engines and Work

• The Carnot cycle allows maximum heat to work conversion
• Compressing an ideal gas isothermally results in work done on the gas, and heat flows out
• If 300 J of work is done on a system, and 120 J of heat is extracted, the internal energy change is 180 J

Second Law and Entropy

• Free expansion of a gas into a vacuum is an irreversible process
• Entropy of an isolated system can only increase or remain constant
• Entropy measures disorder or randomness
• The second law of thermodynamics states heat cannot spontaneously flow from cold to hot

Spontaneity

• For a spontaneous process, Gibbs Free Energy (ΔG) must be < 0
• The efficiency of a heat engine between T1 and T2 (T2 > T1) cannot exceed 1 - T1/T2

Reversible Processes

• In a reversible process, the system transitions via a series of equilibrium states
• The entropy change for the reversible isothermal expansion of 2 mol of an ideal gas from 10 L to 20 L is +11.53 J/K, where R = 8.314 J/mol·K

Carnot Engines

• A Carnot engine operating between 400 K and 300 K reservoirs, absorbing 800 J, performs 200 J of work per cycle

Heat Engine Efficiency

• The maximum theoretical efficiency of a heat engine operating between 27°C and 127°C is 25%

Thermodynamic Relations and Potentials

• Gibbs free energy (G) is H - TS
• A process is spontaneous at constant temperature and pressure when ΔH < TΔS
• Gibbs free energy in a system at equilibrium at constant T and P is at a minimum
• At constant temperature and pressure, during a phase change, ΔG = 0
• From the differential of Helmholtz free energy (A = U - TS), the Maxwell relation is (∂S/∂V)T = (∂P/∂T)V

Ideal Gas Processes

• For an ideal gas in an isothermal process, enthalpy change is zero

Chemical Equilibrium

• For a closed system at constant T and P, chemical equilibrium is achieved when dG = 0

Ideal Gas Relationships

• The relationship between Cp and Cv for an ideal gas is Cp - Cv = R

Joule-Thomson Effect

• The Joule-Thomson coefficient for an ideal gas is zero

Clausius-Clapeyron Equation

• The Clausius-Clapeyron equation relates vapor pressure and temperature during phase transition

Applications and Advanced Topics

• The equilibrium constant K is linked to the standard Gibbs free energy change ΔG° by: K = e^(-ΔG°/RT)
• Real gases deviate from ideal behavior at high pressures due to molecular interactions and finite molecular volume

Third Law of Thermodynamics

• According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is zero

Refrigeration Cycles

• For a refrigeration cycle, work must be done to move heat from a cold to a hot reservoir

Spontaneous Processes

• Spontaneous processes are characterized by an increase in the total entropy of the universe

Heat Engine Work

• A heat engine absorbing 1000 J at 500 K and rejecting heat at 300 K has a maximum work output of 400 J

Adiabatic Processes and Ideal Gasses

• For an ideal gas undergoing an adiabatic process, PVᵞ is constant

Monatomic Ideal Gases

• The value of γ (Cp/Cv) for a monatomic ideal gas is 5/3th

Throttling Processes

• Enthalpy remains constant in a throttling (Joule-Thomson) process

Critical Points

• The critical point occurs at the highest temperature where liquid and vapor coexist

Specialized Topics

• The Gibbs-Helmholtz relation is represented by (∂(G/T)/∂T)P = -H/T²
• For an irreversible process between two equilibrium states, ΔS > q/T

Enthalpy and Entropy

• For water vaporizing at 100°C (373 K) with an enthalpy change of 40.7 kJ/mol, the entropy change is 109.2 J/K

Van der Waals Equation

• Constant 'a' in the van der Waals gas equation accounts for the attractive forces between molecules

Equipartition Theorem

• A diatomic gas molecule, considered a rigid rotator, has 5 degrees of freedom at room temperature

Entropy Increase

• Mixing two different gases always increases entropy

Non-Equilibrium Free Energy

• The free energy change for a reaction not at equilibrium is ΔG = ΔG° + RT ln Q

Nernst Equation

• The Nernst equation is used to calculate cell potentials under non-standard conditions

Triple Point of Water

• At the triple point, ice, water, and water vapor coexist in equilibrium

Isothermal Expansion Work

• The work done in a reversible isothermal expansion of n moles of an ideal gas from V₁ to V₂ is -nRT ln(V₂/V₁)