Thermodynamics
Zeroth Law of Thermodynamics
If two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law justifies the use of a **thermometer** to measure temperature.
First Law of Thermodynamics (Energy Conservation)
The First Law states that **energy** in a closed system is conserved. It relates the change in internal energy ($\Delta E$) to the heat transfer ($Q$) and work ($W$).
ΔE = Q − W
*Note: This sign convention uses Q as heat added *to* the system and W as work done *by* the system.*
Enthalpy and Specific Heat
Enthalpy (H) is defined as H = U + PV, where U is the internal energy, P is pressure, and V is volume. It represents the total heat content of a system.
The **specific heat at constant pressure ($c_p$)** and the **specific heat at constant volume ($c_v$)** are related for an ideal gas:
cp − cv = R (Mayer's Relation)
γ = cp / cv (Adiabatic Index or Ratio of Specific Heats)
Second Law of Thermodynamics
Heat cannot spontaneously flow from a colder body to a hotter body (**Clausius Statement**). Entropy always increases in an isolated system. The **Kelvin-Planck Statement** says it's impossible to construct an engine operating in a cycle that produces no effect other than the extraction of heat from a reservoir and the performance of an equal amount of work.
The Carnot Cycle and Efficiency
The **Carnot cycle** is the most efficient possible cycle for converting heat into work. The efficiency ($\eta$) of a reversible engine operating between two absolute temperatures ($T_H$ and $T_L$) is:
ηCarnot = 1 − (TL / TH)
Where TL is the absolute temperature of the cold reservoir and TH is the absolute temperature of the hot reservoir.
Third Law of Thermodynamics
The entropy of a perfect crystal at absolute zero temperature (0 Kelvin) is exactly zero. This law provides a datum for the determination of entropy.
