Ablue supergiant star has surface temperature 27 kk and has total power output 1 times that of the sun.
a. where is the wien peak of this star's blackbody curve? λmax =
b. given the sun's 6.96×108m radius, what's the radius of the supergiant? r =

Wien peak ( λmax ) is 107.40 nm

radius of super giant is 1.086 × m

Explanation:

given data

temperature 27 kK

power = 100000 times of Sun

Sun radius =  6.96 × 10^8 m

to find out

Wien peak ( λmax ) and radius of supergiant (r)

solution

we will apply here first wien law to find Wien peak  that is

λmax = b / t

λmax = 2.9 × / 27000 = 1.0740 ×

so Wien peak ( λmax ) is 107.40 nm

and

now we apply steafay law that is

P = σ × A ×   .........................1

and we know total power output 100000 time of Sun

so we say  

4πr²s  = 100000 × 4πR²s

r² = 100000  × R² /

put here value

r² = 100000  × (6.96× )² × /

r² = 1.18132 ×

r = 1.086 × m

so radius of super giant is 1.086 × m

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle