Thermodynamics Flow Chart (Modular with LaTeX)
1. Ideal Gas Laws and Entropy
graph TD
A1["$pV = nRT$"]
A2["$w_{on} = -nRT\\ln\\left(\\frac{V_f}{V_i}\\right)$"]
A3["$q_{in} = nRT\\ln\\left(\\frac{V_f}{V_i}\\right)$"]
A4["$\\Delta S = nR\\ln\\left(\\frac{V_f}{V_i}\\right)$"]
A5["$\\Delta S = c\\ln\\left(\\frac{T_f}{T_i}\\right)$"]
A6["$\\Delta S = \\int \\frac{C}{T} dT$"]
A1 --> A2
A2 --> A3
A3 --> A4
A5 --> A6
2. Thermodynamic Potentials
graph TD
B1["$dU = TdS - pdV$"]
B2["$dG = Vdp - SdT$"]
B3["$\\Delta G = \\Delta H - T\\Delta S$"]
B4["$\\Delta H = \\Delta U + p\\Delta V$"]
B5["$H = U + nRT$"]
B6["$H_m = U_m + RT$"]
B7["$\\frac{H_m}{T}$"]
B8["$\\frac{U_m}{T}$"]
B1 --> B4
B4 --> B3
B5 --> B6
B6 --> B7
B6 --> B8
3. Energy, Work and Heat
graph TD
C1["$\\Delta U = q_{in} - p\\Delta V$"]
C2["$\\Delta U = q_{in} + w_{on}$"]
C3["$w_{on} = -p\\Delta V$"]
C4["$\\Delta U = q_V$"]
C5["$\\Delta H = q_p$"]
C3 --> C1
C1 --> C2
C1 --> C4
C2 --> C4
C4 --> C5
4. Heat Capacity and Relationships
graph TD
D1["$q = C \\Delta T$"]
D2["$C = \\frac{q}{\\Delta T}$"]
D3["$C_V = \\frac{\\Delta U}{\\Delta T}$"]
D4["$C_p = \\frac{\\Delta H}{\\Delta T}$"]
D5["$C_{p,m} = C_{V,m} + R$"]
D6["$C_s = \\frac{C}{m}$"]
D7["$C_m = \\frac{C}{n}$"]
D1 --> D2
D2 --> D3
D2 --> D4
D4 --> D5
D2 --> D6
D2 --> D7
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