Question

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)

Answer 1

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

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

G is the universal gravitational constant,

M is the mass of the planet

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

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

M_m= 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)