The root-mean-square speed of the molecules in a gas in an indication of the tem

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.

In which way does this trend agree with the trend shown in Fig. 10.15 of the textbook?

2) Stars are primarily made of Hydrogen. Calculate vrms for the three stars shown in the figure above. How do these values compare to the rms speed of Hydrogen at room temperature?

Explanation / Answer

The figure 10.15 is not identified but the trend should be very correlated

The rms speed of hydrogen molecules at room temperature(20oC) and atmspheric pressure is

vrms = (3RT/M)1/2

Here,R = 8.31 J/(mol.K),T = 20oC = 20 + 273 = 293 Kand M = 1.0079 g/mol = 1.0079 * 10-3 kg/mol

or vrms = [(3 * 8.31 * 293)/(1.0079 *10-3)]1/2

or vrms = 2692 m/s

At T=310 K

vrms = [(3 * 8.31 * 310)/(1.0079 *10-3)]1/2

v=2769.06 m/s

At T=3000 K

vrms = [(3 * 8.31 * 3000)/(1.0079 *10-3)]1/2

v=8614.16 m/s

At T=5800 K

vrms = [(3 * 8.31 * 5800)/(1.0079 *10-3)]1/2

v=11977.5 m/s

AT T=15000 K

vrms = [(3 * 8.31 * 15000)/(1.0079 *10-3)]1/2

v=19261.85 m/s

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