As the derivative move toward -1, the band gap increases (because ln(|x|) has a zero at x=1 with a positive gradient). In this case the higher temperature curve has a higher band gap. As temperature decreases the band gap decreases. The graph shows increasing temperature widen the band gap and move the emitted spectrum towards the ultra-violet band.
If quanta are created with \(\cfrac{d\,T}{d\,t}\), a strong variation in \(T\), \(E_{BG}\) will vary through a wide bandwidth and is likely to be white light.
