Molecular Physics and Thermodynamics
Core concepts
The kinetic-molecular model links macroscopic quantities to molecular motion: pressure arises from molecular collisions, and absolute temperature is proportional to average translational kinetic energy, (3/2)kT per molecule. The ideal gas law, pV = nRT (or pV = NkT), connects state variables. Remember that T must be in kelvin.
The first law of thermodynamics, ΔU = Q − W (with W the work done by the gas), is the central accounting rule. Work done by a gas at constant pressure is W = pΔV. For isochoric processes W = 0; for isothermal processes ΔU = 0; for adiabatic processes Q = 0. Internal energy of an ideal gas depends only on temperature.
Heat capacity: Q = mcΔT for a substance; molar heat capacities differ at constant volume and constant pressure (C_p = C_v + R for ideal gases).
The second law introduces entropy and the direction of spontaneous processes; heat flows from hot to cold without external work.
Traps
- Using Celsius where kelvin is required.
- Confusing work done by the gas with work done on the gas (sign of W).
- Assuming ΔU = 0 in every process, not just isothermal ones.
- Forgetting that in an isothermal process heat can be exchanged even though temperature is constant.
- Mixing up the latent heat of fusion and vaporization.
Worked rule of thumb
For a cyclic process, the net change in internal energy over one full cycle is zero, so Q_net = W_net. The area enclosed by the cycle on a p–V diagram equals the net work done.