Question

The root-mean-square speed of the molecules in a gas in an indication of the temperature of this gas. Shown below is the spectrum of three stars of different surface temperature. The x-axis displays the wavelength of the light emitted by the star. Shorter wavelength corresponds to higher energy of the gas, longer wavelength to lower energy. Stars are primarily made of Hydrogen. Calculate vrms for the three stars shown in the figure. How do these values compare to the rms speed of Hydrogen at room temperature?

Answer 1

The rms speed of the molecules in a gas is, 3RT ms The rms speed of the hydrogen molecules at room temperature is, 3RT VH 3(8.314 J/mole-K)(20 +273) K 1 g/mole 85.5 m/s The rms speed of the molecules on the surface of the 3000 K star is, 3RT 3000 K 3(8.314 J/ mole K) (3000 ) 1 g/mole 273.5 m/s The comparison this speed with the rms speed of the hydrogen molecules at room temperature 1s, 13000 K _273.5 m/s 85.5 m/s -3.2 '3000 K-3.2VH

The rms speed of the molecules on the surface of the Sun is, 3RT un 3(8.314 J/mole K) (5800 K) 1 g/mole 380 m/s The comparison this speed with the rms speed of the hydrogen molecules at room temperature is, VSun 380 m/s VH85.5 m/s sun 4.41 The rms speed of the molecules on the surface of the 15,000 K is 3RT 15000 K M 3(8.314 Jmole K) (15,000 K) 1 g/mole 611.6 m/s The comparison this speed with the rms speed of the hydrogen molecules at room temperature 1s, 0 611.6 m/s 85.5 m/s 1.15 15000x7.151