Final answer:
The hottest stars on the H-R Diagram are of spectral class O, with temperatures over 28,000 K. The coolest stars are of spectral class M, with temperatures below 3500 K. Luminosity increases the most from spectral types M to O compared to mass.
Step-by-step explanation:
The hottest stars on the Hertzsprung-Russell (H-R) Diagram belong to spectral class O. These O-type stars have surface temperatures exceeding 28,000 K, and they are characterized by the presence of ionized helium and highly ionized atoms in their spectra. The spectral classes proceed from hottest to coolest as follows: O, B, A, F, G, K, and M, with three additional classes, L, T, and Y, for even cooler objects such as brown dwarfs. An O0 star would be the hottest within the O class, and a M9 star would be the coolest within the main-sequence class before transitioning to L-type brown dwarfs. As the temperature decreases, the spectral features change, with absorption bands of different elements becoming prominent.
The coolest stars are found in spectral class M, with temperatures below 3500 K and prominent absorption bands of titanium oxide. Along the main sequence, stars' mass and luminosity both increase from spectral type M to O, but luminosity changes by the largest factor. The most luminous stars are of spectral type O due to their massive size and high surface temperature, while spectral type M consists of the least luminous stars due to their smaller mass and cooler temperatures.