• word_count: 200

In an isobaric process (constant pressure), the gas expands or compresses while maintaining $P = \text{constant}$. Work: $W = P\Delta V = nR\Delta T$. Heat: $Q = nC_p\Delta T$. Internal energy change: $\Delta U = nC_v\Delta T$. Verification via the First Law: $nC_p\Delta T = nC_v\Delta T + nR\Delta T$, which gives Mayer's relation $C_p = C_v + R$. On a P-V diagram, an isobaric process is a horizontal line.

In an isochoric process (constant volume), no work is done ($W = P\Delta V = 0$ since $\Delta V = 0$). The First Law reduces to $Q = \Delta U = nC_v\Delta T$ — all heat goes directly into changing internal energy. On a P-V diagram, an isochoric process is a vertical line. Gay-Lussac's law applies: $P/T = \text{constant}$.

The key contrast: at constant pressure, only a fraction $C_v/C_p = 1/\gamma$ of the supplied heat raises the temperature (the rest does expansion work). At constant volume, 100% of the heat raises the temperature. This is why $C_p > C_v$ — more heat is needed at constant pressure to achieve the same temperature rise because energy is "diverted" to mechanical work.