Physics

The key insight is that volumetric expansion coefficient $\beta = \frac{1}{V}\frac{dV}{dT}$ measures the fractional change in volume per degree—not the absolute change. At constant pressure, an ideal gas obeys $V \propto T$, so the volume does grow faster at higher temperatures in absolute terms. However, because the gas is already much larger at high temperature, that same absolute expansion represents a smaller fraction of the total volume, making $\beta$ itself decrease. Think of it as the difference between adding one liter to a 10-liter tank versus a 100-liter tank.

The key insight is that volumetric expansion coefficient $\beta = \frac{1}{V}\frac{dV}{dT}$ measures the fractional change in volume per degree—not the absolute change. At constant pressure, an ideal gas obeys $V \propto T$, so the volume does grow faster at higher temperatures in absolute terms. However, because the gas is already much larger at high temperature, that same absolute expansion represents a smaller fraction of the total volume, making $\beta$ itself decrease. Think of it as the difference between adding one liter to a 10-liter tank versus a 100-liter tank.