Solution of Solar Corona Conductivity Problem

Following on from the blog to do with the solar corona, e.g.

http://brane-space.blogspot.com/2012/04/conductivity-in-solar-corona.html

We had the problem at the very end:

Find the temperature of the corona at the distance r = 2R_o. From this estimate the flux at this distance.


Solution:

Recall the temperature at distance r is given by:

T(r) = T_o (R_o / r) ^2/7


Then at a distance, r = 2R_o:

T(r) =  (2 x 10⁶ K) (R_o /2 R_o ) ^2/7

T(r) =  (2 x 10⁶ K) (1 /2 ) ^2/7 =   1.6 x 10⁶ K

To get the flux, we assume: F = 2/7 [4 π R k T ]


Where: k = 1.8 x 10-10 (T ^5/2 / ln Z) W m^-1 K^-1


k = 1.8 x 10^-10 [(1.6 x 10^6 K) ^5/2 / 20] W m^-1 K^-1


k = 3. 1 x 10^4 W m^-1 K^-1

Therefore: the flux F =

2/7 [4 π (14 x 10^8 m) (1. 1 x 10 ^3 W m^-1 K^-1) (1.6 x 10^6 K)]


F = 2.5 x 10 ^20 W