Physics Thermodynamic.md

1. Energy, Entropy, and the Main Laws of Thermodynamics

• Temperature Conversion (Celsius to Kelvin):

  • Formula: $T[K] = T[°C] + 273$
  • Variables: $T[K]$ = Temperature in Kelvin, $T[°C]$ = Temperature in Celsius.

• Entropy (S): A measure of the disorder of a system.

  • Formula: $ΔS = Q_{Rev} / ΔT$
  • Variables: $ΔS$ = Change in entropy, $Q_Rev$ = Amount of heat in a reversible process, $ΔT$ = Change in temperature.
  • Unit: J/K (Joules per Kelvin).

• Internal Energy (U): The total energy available for thermodynamic processes.

  • Formula: $ΔU = Q + W$
  • Variables: ΔU = Change in internal energy, Q = Heat, W = Work done on the system.
  • Unit: J (Joule).

• Specific Heat Capacity (c): A constant indicating how much heat a substance can store.

  • Formula: $c = ΔQ / (m × ΔT)$
  • Variables: c = Specific heat capacity, ΔQ = Change in heat, m = Mass, ΔT = Change in temperature.
  • Unit: J/(kg×K).

• Heat Flux (Thermal Conduction): The amount of heat flowing through a material.

  • Formula: $Q = λ × A × ΔT / l$
  • Variables: Q = Heat flux, λ = Thermal conductivity, A = Cross-sectional area, ΔT = Temperature difference, l = Length of the distance.
  • Unit: W (Watt).

2. Thermodynamics of Chemical Reactions

• Enthalpy (H): The heat content of a system.

  • Formula: $H = U + P × V$
  • Variables: H = Enthalpy, U = Internal energy, P = Pressure, V = Volume.
  • Unit: kJ/mol.

• Enthalpy of Reaction (ΔH): The change in heat during a reaction.

  • Formula: $ΔH_{Reaction} = H_{Products} – H_{Reactants}$
  • Note: ΔH < 0 is an exothermic reaction (releases heat); ΔH > 0 is an endothermic reaction (absorbs heat).

• Gibbs Energy (G): Determines if a reaction can occur spontaneously.

  • Formula: $ΔG = ΔH – T × ΔS$
  • Variables: ΔG = Change in Gibbs energy, ΔH = Change in enthalpy, T = Temperature, ΔS = Change in entropy.
  • Unit: kJ/mol.
  • Note: ΔG < 0 is an exergonic reaction (spontaneous); ΔG > 0 is an endergonic reaction (not spontaneous).

• Gibbs Energy from Equilibrium Constant (k):

  • Formula: $ΔG = -R × T × ln(k)$
  • Variables: R = Gas constant, T = Temperature, k = Equilibrium constant.
  • Unit: kJ/mol.

• Gibbs Energy for Redox Reactions:

  • Formula: $ΔG = -z × F × ΔE_{0}$
  • Variables: z = Number of transferred electrons, F = Faraday constant, ΔE0 = Difference in standard potentials.
  • Unit: kJ/mol.

3. Gases

• General Gas Equation (Ideal Gas Law):

  • Formula: $p × V = n × R × T$
  • Variables: p = Pressure, V = Volume, n = Amount of substance (moles), R = Gas constant (8.314 J/(mol×K)), T = Temperature.

• Simplified Gas Law (for constant temperature and amount of gas):

  • Formula:$p_1 × V_1 = p_2 × V_2$
  • Variables: p_1, V_1 = Initial pressure and volume; p_2, V_2 = Final pressure and volume.

• Dalton's Law of Partial Pressures: The total pressure of a gas mixture is the sum of the partial pressures.

  • Formula for Total Pressure: $p_total = p_1 + p_2 + p_3 + …$
  • Formula for Partial Pressure: $p_i = (p_{total} × V_i) / V_{total}$

• Average Particle Velocity in a Gas:

  • Formula: $v = √(8 × R × T / (π × M))$
  • Variables: v = Average velocity, R = Gas constant, T = Temperature, M = Molar mass.
  • Unit: m/s.

• Average Kinetic Energy of a Gas Particle:

  • Formula: $E_{kin} = 3/2 × k_b × T$
  • Variables: $E_{kin}$ = Kinetic energy, $k_b$ = Boltzmann constant, T = Temperature.
  • Unit: J (Joule).

4. Humidity

• Absolute Humidity (f):

  • Formula: $f = m_{\text{water vapor}} / V$
  • Variables: $m_{\text{water vapor}}$ = Mass of water vapor, V = Volume.
  • Unit: g/m³.

• Relative Humidity (f_rel):

  • Formula: $f_{rel} = p_{\text{water vapor}} / p_{saturation}$
  • Variables: $p_{\text{water vapor}}$ = Partial pressure of water vapor, $p_{saturation}$ = Saturation vapor pressure at a given temperature.
  • Unit: %.