Question

# What would the surface temperature in degrees Kelvin of the sun have to be so that...

What would the surface temperature in degrees Kelvin of the sun have to be so that the rms velocity of a nitrogen atom at the surface would equal the escape velocity from the sun? (The mass of the sun is 2.0x1030 kg and the radius of the sun is 7.0x108 m. The nitrogen atom has a mass equal to 14 protons)

rms velocity of nitrogen atom at the surface = escape velocity of the sun

Escape velocity of the sun = Vesc = ------------------- (i)

G is the universal gravitational constant,

M is the mass of the planet

(RSun) is distance of the point, from the centre of the planet, from which the mass is to be projected.

rms velocity of nitrogen = Vrms = --------------------(ii)

Mm= molar mass of the gas in kilograms per mole,( in this case nitrogen = 2.8*10-4 kg/mol)

R = molar gas constant

T= temperature in Kelvin.

On equating (i) and (ii),

=

= =

T = 15 million K (approx)

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