If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This defines temperature.

Kelvin-Planck Statement: It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.
Clausius Statement: It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.
Entropy ($S$): Measure of disorder or randomness.
- For a reversible process: $dS = \frac{\delta Q}{T}$.
- For an irreversible process: $dS > \frac{\delta Q}{T}$.
- The entropy of an isolated system never decreases; it either increases or remains constant ($\Delta S_{isolated} \ge 0$).
Carnot Cycle (Reversible Cycle): Most efficient cycle operating between two temperature reservoirs.
- Consists of two isothermal and two adiabatic processes.
- Carnot Efficiency: $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$. ($T_C$ and $T_H$ are absolute temperatures).
Availability (Exergy): Maximum useful work that can be obtained from a system as it comes into equilibrium with its surroundings.

Ideal Gas Law: $PV = nRT$ or $PV = mRT$.
- $P$: Absolute pressure, $V$: Volume, $n$: Moles, $m$: Mass.
- $R$: Specific gas constant ($R = R_u/M$, where $R_u$ is universal gas constant and $M$ is molar mass).
- $T$: Absolute temperature.
Boyle's Law: $PV = \text{constant}$ (at constant $T$).
Charles's Law: $V/T = \text{constant}$ (at constant $P$).
Specific Heats:
- $C_p$: Specific heat at constant pressure.
- $C_v$: Specific heat at constant volume.
- Relation: $C_p - C_v = R$.
- Ratio of Specific Heats: $\gamma = C_p / C_v$.

Constant Volume (Isochoric):
- $\delta W = 0$
- $Q = \Delta U = m C_v \Delta T$
Constant Pressure (Isobaric):
- $W = P \Delta V$
- $Q = \Delta H = m C_p \Delta T$
Constant Temperature (Isothermal):
- $\Delta U = 0$ (for ideal gas)
- $Q = W = P_1 V_1 \ln\left(\frac{V_2}{V_1}\right) = P_1 V_1 \ln\left(\frac{P_1}{P_2}\right)$
Adiabatic (Isentropic for Reversible): No heat transfer ($\delta Q = 0$).
- $PV^\gamma = \text{constant}$
- $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$
- $T_1 P_1^{(1-\gamma)/\gamma} = T_2 P_2^{(1-\gamma)/\gamma}$
- $W = \frac{P_1 V_1 - P_2 V_2}{\gamma - 1} = \frac{mR(T_1 - T_2)}{\gamma - 1}$
- $\Delta U = -W$
Polytropic: $PV^