Points to Ponder

The temperature of an object depends on its average internal energy — the random, microscopic motion of its atoms and molecules. It has nothing to do with the kinetic energy of the object as a whole. A bullet speeding through the air is not hotter because of its high speed; its centre-of-mass motion contributes nothing to its temperature.

Thermodynamic equilibrium is a condition where the macroscopic state variables — pressure, volume, temperature — do not change with time. This is different from mechanical equilibrium, which only requires that the net external force and net external torque on the system be zero. A system can be in mechanical equilibrium but not in thermodynamic equilibrium (e.g., a gas with a temperature gradient inside a rigid container).

Even when a system is in thermodynamic equilibrium (macroscopic variables are steady), its microscopic constituents — molecules, atoms — are in constant, chaotic motion. They are not in mechanical equilibrium; they collide and exchange energy continuously. Equilibrium at the macro level does not imply stillness at the micro level.

The heat capacity of a substance is not a fixed number; it depends on the specific process by which heat is added or removed. For example, the heat capacity at constant volume ($C_V$) is different from the heat capacity at constant pressure ($C_P$). The path matters. …