Energy and Thermodynamics

Energy

• The capacity to do work, existing as heat, light, electricity, and chemical forms.
• Kinetic energy (KE) is the energy of motion, defined as $KE = 1/2 \cdot mv^2$.
• Potential energy (PE) is stored energy, defined as $PE = mgh$.
• Energy is measured in Joules (J), where $1 J = 1 kg \cdot m^2/s^2$, or in calories (cal), where $1 cal = 4.184 J$.

Thermodynamic Systems

• A system is the part of the universe of interest.
• The surroundings are the rest of the universe outside the system.
• Open systems exchange both matter and energy with surroundings.
• Closed systems exchange energy but not matter.
• Isolated systems exchange neither energy nor matter.

State Functions

• Properties that depend only on the current state, not on how it was achieved, such as energy, pressure, volume, and temperature.
• Changes in state functions are independent of path: $\Delta U = U_{final} - U_{initial}$.

First Law of Thermodynamics

• Energy is conserved, meaning it can be converted but not created or destroyed.
• $\Delta U = q + w$, where
  • $\Delta U$ is the change in internal energy of the system
  • $q$ is heat added to or removed from the system
  • $w$ is work done on or by the system

Enthalpy

• Measures heat content of a system at constant pressure, defined as $H = U + PV$.
• Under constant pressure, $\Delta H = \Delta U + P\Delta V = q_p$.
• Exothermic processes release heat $(\Delta H < 0)$.
• Endothermic processes absorb heat $(\Delta H > 0)$.
• Units of enthalpy are Joules (J) or Kilojoules (kJ).
• Standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when 1 mole of a compound is formed from its elements in their standard states (1 atm and 298 K).
• $\Delta H^\circ = \sum n \Delta H_f^\circ (products) - \sum n \Delta H_f^\circ (reactants)$.

Calorimetry

• Calorimetry measures heat flow using $q = mc\Delta T$.
  • $q$ is heat absorbed or released
  • $m$ is mass
  • $c$ is specific heat capacity
  • $\Delta T$ is change in temperature
• Bomb calorimeters measure heat at constant volume: $q = C\Delta T$, where $C$ is the heat capacity of the calorimeter.

Hess's Law

• The enthalpy change of an overall process is the sum of enthalpy changes of its individual steps: $\Delta H_{overall} = \Delta H_1 + \Delta H_2 +...$
• Reversing a reaction changes the sign of $\Delta H$.

Entropy

• Measures the disorder or randomness of a system, defined as $\Delta S = q_{rev}/T$.
  • $q_{rev}$ is heat absorbed or released in a reversible process
  • $T$ is absolute temperature
• Entropy is measured in Joules per Kelvin (J/K).
• Entropy increases with:
  • Increasing temperature
  • Increasing volume
  • Increasing number of particles
  • Change of state from solid to liquid to gas
• Standard entropy change: $\Delta S^\circ = \sum nS^\circ (products) - \sum nS^\circ (reactants)$.

Second Law of Thermodynamics

• The entropy of the universe increases in any spontaneous process: $\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0$.

Gibbs Free Energy

• Measures the spontaneity of a process: $G = H - TS$ and $\Delta G = \Delta H - T\Delta S$.
• Spontaneous process: $\Delta G < 0$.
• Non-spontaneous process: $\Delta G > 0$.
• Equilibrium: $\Delta G = 0$.
• Standard free energy change: $\Delta G^\circ = \sum n \Delta G_f^\circ (products) - \sum n \Delta G_f^\circ (reactants)$.

Free Energy and Equilibrium

• $\Delta G = -RTlnK$, where
  • $R$ is the ideal gas constant (8.314 J/mol·K)
  • $T$ is absolute temperature
  • $K$ is the equilibrium constant
• If $K > 1$, products are favored $(\Delta G < 0)$.
• If $K < 1$, reactants are favored $(\Delta G > 0)$.
• If $K = 1$, equilibrium $(\Delta G = 0)$.

Temperature Dependence of Equilibrium Constant

• van't Hoff equation relates changes in the equilibrium constant with temperature to changes in enthalpy: $ln(K_2/K_1) = -\Delta H^\circ/R (1/T_2 - 1/T_1)$.