Cue Column | Notes Column

What is the first law? | Energy is conserved: $\Delta U = q + w$. Heat absorbed BY system ($q > 0$); work done ON system ($w > 0$).

Three work expressions | 1. Free expansion: $w = 0$ (no $P_{ext}$); 2. Irreversible: $w = -P_{ext}\Delta V$; 3. Reversible isothermal: $w = -nRT\ln(V_2/V_1)$

Ideal gas isothermal | $\Delta U = 0$ because $U$ is only a function of temperature for ideal gases.

IUPAC trap | Older convention: $\Delta U = q - w$ (work done BY system positive). NCERT uses IUPAC: $\Delta U = q + w$ (work ON system positive).

Key dimensional check | $w = nRT\ln(V_2/V_1)$: mol × J/(mol·K) × K = J ✓

Summary

The first law is energy conservation for thermodynamic systems. Internal energy $\Delta U$ changes only through heat and work. For ideal gases in isothermal processes, $\Delta U = 0$ and $q = -w$.

Apparatus Reference