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 2.0x10^{30} kg and the radius of the sun is
7.0x10^{8} 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)

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