Thermodynamics

Essential formulas and concepts in thermodynamics

First Law of Thermodynamics

\(\displaystyle \Delta U = Q - W\)

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Boltzmann’s Entropy Formula

\(S = k_B \ln \Omega\)

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Ideal Gas Law

\(P V = n R T\)

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Equation of state for an ideal gas (point particles, no intermolecular forces). It combines Boyle’s law, Charles’s law, etc. Tells, for example, how pressure increases with temperature if volume is fixed.

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Thermal Expansion (Linear)

\(\Delta L = \alpha L_0 \Delta T\)

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Carnot Engine Efficiency (Max Theoretical)

\(\displaystyle \eta_{\text{Carnot}} = 1 - \frac{T_c}{T_h}\)

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