First Law of Thermodynamics
$$\Delta Q = \Delta U + \Delta W \implies dQ = dU + P\,dV$$
- Mayer's Formula: $C_p - C_v = R$
- Adiabatic Process: $P V^\gamma = \text{constant}$ (Work done: $W = \frac{P_1V_1 - P_2V_2}{\gamma - 1}$)
- Carnot Engine Efficiency ($\eta$):
$$\eta = 1 - \frac{T_2}{T_1}$$
