Thermodynamics Cheatsheet

Cheat Codes & Shortcuts

• First Law: \( \Delta U = Q - W \), internal energy change equals heat added minus work done.
• Second Law: Entropy of an isolated system never decreases, \( \Delta S \geq 0 \).
• Work: For an ideal gas, \( W = P \Delta V \) (isobaric process).
• Ideal Gas Law: \( PV = nRT \), relates pressure, volume, moles, and temperature.
• Carnot Efficiency: \( \eta = 1 - \frac{T_C}{T_H} \), for a Carnot engine.
• Enthalpy: \( H = U + PV \), useful for constant pressure processes.
• Entropy Change: \( \Delta S = \int \frac{dQ_{rev}}{T} \), for reversible processes.
• Gibbs Free Energy: \( G = H - TS \), determines spontaneity at constant T, P.
• Heat Capacity: \( C = \frac{dQ}{dT} \), at constant volume or pressure.
• Adiabatic Process: \( PV^\gamma = \text{constant} \), where \( \gamma = \frac{C_P}{C_V} \).

Quick Reference Table

Type	Formula	Description
First Law	\( \Delta U = Q - W \)	Energy conservation: internal energy change.
Ideal Gas	\( PV = nRT \)	Relates state variables for ideal gases.
Carnot Cycle	\( \eta = 1 - \frac{T_C}{T_H} \)	Maximum efficiency of a heat engine.
Entropy	\( \Delta S = \int \frac{dQ_{rev}}{T} \)	Entropy change for reversible processes.
Adiabatic	\( PV^\gamma = \text{constant} \)	No heat exchange, \( \gamma = \frac{C_P}{C_V} \).
Gibbs Energy	\( \Delta G = \Delta H - T \Delta S \)	Spontaneity at constant T, P.

Advice

Thermodynamics Quick Tips

• First Law: Always account for both heat and work in energy balance.
• State Variables: Use \( PV = nRT \) to relate P, V, T for ideal gases.
• Entropy: For reversible processes, compute \( \Delta S = \int \frac{dQ}{T} \).
• Efficiency: Carnot efficiency sets the upper limit for heat engines.
• Free Energy: Use Gibbs or Helmholtz to predict spontaneity.

Thermodynamics Speed Quiz

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