Summary

• Zeroth Law: If $A$ and $B$ are each in thermal equilibrium with $C$, then $A$ and $B$ are in thermal equilibrium with each other. This defines temperature as a measurable property.

• Heat and Work — Sign Convention: If $Q>0$, heat is added to the system. If $Q<0$, heat is removed from the system. If $W>0$, work is done by the system. If $W<0$, work is done on the system.

• First Law: Energy is conserved. $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system.

• Second Law (Kelvin-Planck): No cyclic process can convert heat completely into work without other effects. (Clausius): No cyclic process can transfer heat from a colder to a hotter body without external work.

• Reversible vs Irreversible: Reversible processes occur through infinitesimal steps with no dissipation; irreversible processes involve friction, unrestrained expansion, or finite temperature differences.

• Calorie: 1 calorie is the amount of heat required to raise the temperature of 1 g of water from 14.5°C to 15.5°C. 1 cal = 4.186 J.

• Heat Capacity: $C = \frac{Q}{\Delta T}$. For ideal gases: $C_P - C_V = nR$ (Mayer's relation). $\gamma = \frac{C_P}{C_V}$.

• Molar Specific Heat of Solids (Equipartition): Modelling a solid as $N$ atoms, each a 3-D oscillator, the equipartition theorem gives a molar specific heat $C = 3R$, which generally agrees with experiment at ordinary temperatures (the Law of Dulong and Petit).

• Adiabatic Process: $Q = 0$. For an ideal gas: $PV^\gamma = \text{constant}$, $TV^{\gamma-1} = \text{constant}$, $T^\gamma P^{1-\gamma} = \text{constant}$.

• Isothermal Process: $\Delta T = 0$, $\Delta U = 0$, so $Q = W = nRT \ln\left(\frac{V_f}{V_i}\right)$.

• Carnot Engine: Most efficient reversible engine operating between $T_1$ (source) and $T_2$ (sink). Efficiency $\eta = 1 - \frac{T_2}{T_1}$.

• Key Formulas:

  • Work in isobaric process: $W = P\Delta V$
  • Efficiency of any heat engine: $\eta = 1 - \frac{Q_2}{Q_1}$

Quantities used in this chapter

| Quantity | Symbol | Dimensions | Unit | Remark |

|---|---|---|---|---| …