Which gives off more heat, you, or the Sun? If we're talking about net heat, it's obviously the Sun, but if we're talking about heat output per unit mass, it's not so clear. Calculate the ratio of your body's heat output per unit mass to that of the Sun.
Details and Assumptions
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I did not know the difference but got right answer by using both values one by one.Thanks
Dear Michael Mendrin, Nothing can stop your intelligence to know what people meant to you. I confess that there was a subconscious meaning but it was also a semi-intention. Please forget it and do accept my semi-apology. Thanks! Lu Chee Ket
P = A σ T 4
A = 4 π R 2 = 4 π ( 7 × 1 0 8 ) 2 = 6 . 1 5 7 5 2 1 6 0 1 0 3 5 9 9 × 1 0 1 8 m 2
T 4 = 5 7 8 0 4 = 1 1 1 6 1 2 1 1 9 0 5 6 0 0 0 0 K 4
P = 6 . 1 5 7 5 2 1 6 0 1 0 3 5 9 9 × 1 0 1 8 × 5 . 7 × 1 0 − 8 × 1 1 1 6 1 2 1 1 9 0 5 6 0 0 0 0 = 3 . 8 9 6 9 8 6 7 1 8 6 7 4 8 6 × 1 0 2 6 W .
2 × 1 0 3 0 k g 3 . 8 9 6 9 8 6 7 1 8 6 7 4 8 6 × 1 0 2 6 W = 1 . 9 4 8 4 9 3 3 5 9 3 3 7 4 3 × 1 0 − 4 W / k g
Since 2000 Calories = 2000 × 4184 Joules = 8368000 J,
2 4 × 3 6 0 0 8 3 6 8 0 0 0 = 9 6 . 8 5 1 8 5 1 8 5 1 8 5 1 9 W ;
7 5 k g 9 6 . 8 5 1 8 5 1 8 5 1 8 5 1 9 W = 1 . 2 9 1 3 5 8 0 2 4 6 9 1 3 6 W / k g
Ratio = 1 . 9 4 8 4 9 3 3 5 9 3 3 7 4 3 × 1 0 − 4 1 . 2 9 1 3 5 8 0 2 4 6 9 1 3 6 = 6 . 5 9 3 0 2 1 7 4 1 6 9 2 3 1 E + 3
With 5 . 6 7 0 3 7 3 × 1 0 − 8 instead of 5 . 7 × 1 0 − 8 , 6 . 6 2 7 4 6 9 4 6 7 6 4 2 8 1 E + 3 is obtainable.
This ratio may give reasonable fact of why the sun can last for a long period of time in space.
Answer: 6 5 9 3 e l s e 6 6 2 7
The question may mention significant figures wanted.
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Okay, that was a little weird.
Edit: Here's how it's worked out
M = 2 × 1 0 3 0 × k g
R = 7 × 1 0 8 × m e t e r
T = 5 7 8 0 × k e l v i n
C a l o r i e = 1 0 0 0 ( 0 . 0 0 1 1 6 2 2 2 ) × w a t t × h o u r
σ = 5 . 6 7 0 3 7 3 × 1 0 − 8 w a t t × m e t e r − 2 × k e l v i n − 4
σ is the Stefan-Boltzman constant
Total radiated energy from sun in 2 4 hour period divided by sun’s mass
S u n = M 2 4 × h o u r ( 4 π R 2 σ T 4 )
Total radiated energy from body in 2 4 hour period divided by body’s mass
B o d y = 7 5 × k g 2 0 0 0 × C a l o r i e
Ratio of Body to Sun
S u n B o d y = 6 6 2 7 . 4 6 . . .
which is a dimensionless ratio, i.e., all the physical dimensions drop out
Note: Calorie, with capital "C", is 1 0 0 0 times greater than calorie, with lower case "c". Calories is commonly used for foods, while calories is used for stuff like locomotive steam engine thermodynamic analysis. Maybe that explains why that family is glowing so much.