Classification of Thermodynamic Processes

A thermodynamic process is classified by which variable is held constant (or which quantity is forced to be zero). Each process type has one simplifying constraint that dramatically reduces the number of unknowns in the first law.

Isothermal Process ($\Delta T = 0$)

In an isothermal process, temperature remains constant. For an ideal gas, internal energy depends only on temperature, so $\Delta U = 0$ and $\Delta H = 0$. The entire heat absorbed equals work done by the system ($q = -w$). For reversible isothermal expansion: $w = -nRT\ln(V_2/V_1)$. For irreversible against constant $P_{ext}$: $w = -P_{ext}\Delta V$.

The key comparison: reversible work $>$ irreversible work (in magnitude) between the same initial and final states. This is a direct consequence of the second law.

Adiabatic Process ($q = 0$)

No heat exchange occurs. The entire energy change comes from work alone: $\Delta U = w$. For adiabatic compression (work done ON system), the gas heats up ($\Delta U > 0$). For adiabatic expansion, the gas cools. The work done in adiabatic processes equals $nC_v\Delta T$ for ideal gases.

Isochoric Process ($\Delta V = 0$)

At constant volume, no PV work is performed ($w = 0$). All heat goes into changing internal energy: $\Delta U = q_v = nC_v\Delta T$. A bomb calorimeter operates at constant volume and therefore measures $\Delta U$ directly. To get $\Delta H$, the correction $\Delta n_g RT$ must be applied.

Isobaric Process ($\Delta P = 0$)

At constant pressure, heat equals the enthalpy change: $q_p = \Delta H = nC_p\Delta T$. This is why calorimetry at constant pressure (coffee-cup calorimeter) directly measures $\Delta H$. The extra heat compared to isochoric heating ($nR\Delta T$ per mole) goes into expansion work against constant pressure.

Free Expansion ($P_{ext} = 0$)

When a gas expands into vacuum, no work is done ($w = 0$) and for an ideal gas, no heat is absorbed ($q = 0$), so $\Delta U = 0$. Despite no work or heat, the entropy of the system increases (gas occupies more volume) — demonstrating that entropy generation is possible without heat transfer. This is an irreversible process even though $\Delta U = 0$.

Summary Table