Thermodynamics formulas.

1. First Law of Thermodynamics: ΔU = Q - W
where ΔU is the change in internal energy of a system, Q is the heat added to the system, and W is the work done by the system.

2. Second Law of Thermodynamics: ΔS ≥ Q/T
where ΔS is the change in entropy of a system, Q is the heat added to the system, and T is the temperature at which the heat is added.

3. Ideal Gas Law: PV = nRT
where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature of the gas.

4. Carnot Efficiency: η = 1 - (Tc/Th)
where η is the efficiency of a Carnot heat engine, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir.

5. Entropy Change: ΔS = Qrev/T
where ΔS is the change in entropy of a system, Qrev is the reversible heat added to the system, and T is the temperature at which the heat is added.

First Law of Thermodynamics

- Heat capacity at constant volume: C_v
- Heat capacity at constant pressure: C_p
- Internal energy change: ∆U
- Work done: W
- Heat transferred: Q

```
∆U = Q - W
```

Second Law of Thermodynamics

- Clausius statement: Heat cannot flow spontaneously from a colder to a hotter body.
- Kelvin statement: It is impossible to construct a heat engine that operates in a cycle and does no net work while absorbing energy from a reservoir at a single temperature.

Entropy

- Entropy: S
- Heat transferred at temperature T: Q
- Entropy change: ∆S

```
∆S = Q/T
```

Gibbs Free Energy

- Gibbs free energy: G
- Enthalpy: H
- Temperature: T
- Entropy: S

```
G = H - TS
```

Thermodynamic Properties

- Enthalpy: H = U + PV
- Volume: V
- Pressure: P
- Temperature: T
- Specific heat: c
- Thermal conductivity: k
- Density: ρ
- Adiabatic index: γ

Thermodynamic Relations

- Mayer's relation: C_p - C_v = R
- Poisson's relation: γ = C_p/C_v
- Clapeyron-Clausius equation: dP/dT = ΔH_vap/(TV_vap)
- Stefan-Boltzmann law: P = σT⁴
- Van der Waals equation: P = (RT/(V - b)) - (a/V²)

Thermodynamic Processes

- Adiabatic: No heat transfer (dQ = 0)
- Isothermal: Constant temperature (dT = 0)
- Isobaric: Constant pressure (dP = 0)
- Isochoric: Constant volume (dV = 0)
- Cyclic: Process returns to its initial state