Imagine yourself living in a different solar system, learning about your sun. Yo

Question

Imagine yourself living in a different solar system, learning about your sun. You measure the blackbody spectrum of your sun. and so you know its temperature is T. Furthermore, your astronomers tell you the sun has a radius R. How would you calculate the power output [Watts] of this sun? a. P = sigma(RT)^4 b. P = sigma T^4 4 pi R^2 c. P = sigma T^4/(4 pi R^2) d. P = sigma T^4 (4/3) pi R^3 e. P = 3 sigma T^4/(4 pi R^3) If a solar catastrophe suddenly caused your sun to collapse such that its radius decreased to half its original value, but the power output stayed the same, what would be the new temperature T* of your sun? a. T* = 2T b. T* = 2^2 T c. T* = 2^4 T d. T* = 2^1/2 T e. T* = 2^1/4 T

Explanation / Answer

4Power =sigma*area*T to the power 4

Area=4pi*R*R

P=sigma*4*pi*R*R*T4

So option (b) is correct

5

If power is same and radius is half

Let new temp be T'

Area*Temp to power 4 =constant

R*R*T*T*T*T=(R/2)*(R/2)*T' to power 4

We got T'= 2 to the power (1/2)*T

Option (d) is correct

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