Blundell Thermal Physics · Problem 12.1

In adiabatic processes, the constraint $pV^\gamma = \text{constant}$ captures the interplay between pressure, volume, and temperature without heat exchange. To find the other two relations, use the ideal gas law $pV = nRT$ to eliminate one variable at a time—swapping $p$ for $T$ in the first relation gives you equation (12.23), and then combining both constraints yields (12.24). The key insight is that all three equations describe the same adiabatic path, just expressed in different variable pairs.

In adiabatic processes, the constraint $pV^\gamma = \text{constant}$ captures the interplay between pressure, volume, and temperature without heat exchange. To find the other two relations, use the ideal gas law $pV = nRT$ to eliminate one variable at a time—swapping $p$ for $T$ in the first relation gives you equation (12.23), and then combining both constraints yields (12.24). The key insight is that all three equations describe the same adiabatic path, just expressed in different variable pairs.