Physics

When pressure stays constant, an ideal gas expands as temperature rises—the key is recognizing that volume scales linearly with absolute temperature. Use the ideal gas law ($PV = nRT$) to see that at fixed pressure, $V \propto T$. The coefficient of volumetric expansion $\gamma$ measures the fractional volume change per degree, so you're really asking: how does this rate of expansion depend on temperature? The insight is that $\gamma$ turns out to be independent of temperature for an ideal gas under constant pressure.

When pressure stays constant, an ideal gas expands as temperature rises—the key is recognizing that volume scales linearly with absolute temperature. Use the ideal gas law ($PV = nRT$) to see that at fixed pressure, $V \propto T$. The coefficient of volumetric expansion $\gamma$ measures the fractional volume change per degree, so you're really asking: how does this rate of expansion depend on temperature? The insight is that $\gamma$ turns out to be independent of temperature for an ideal gas under constant pressure.