The earth is getting energy from the sun whose surface temperature is Ts and radius is R. Let the
radius of the earth the r and the distance from the sun be d. Assume the earth and the sun both to
behave as perfect black bodies and the earth is in thermal equilibrium at a constant temperature Te.
Therefore, the temperature Ts of the sun is xTe where x is
[Olympiad 2015 stage-1]
(A)√2d/R
(B)√2R/r
(C)√4d/R
(D)d/r
Answers
Answer:
Explanation:
P = Rate of energy emission by sum = ⊂ × 4πr²T`4
I = Intensity at earth surface = P/ 4πd²
Energy received by earth per second = I × πr²
As the earth is in thermal equilibrium , thus -
Rate of energy absorption = Rate of energy emersion
= I × πr² = ⊂ × 4πr²T`4
= P/ 4πd² × πr² = ⊂ × 4πr²T`4
= ⊂ × 4πR²T`4 / 4πd² = ⊂ × 4πr²T`4
= R²/d²T`4 = 4T`4
√R/dT = (2²)`1/4T
Ts = Te √2d/R
Answer:
Explanation:
P = Rate of energy emission by sum = ⊂ × 4πr²T`4
I = Intensity at earth surface = P/ 4πd²
Energy received by earth per second = I × πr²
As the earth is in thermal equilibrium
, thus -
Rate of energy absorption = Rate of energy emersion
= I × πr² = ⊂ × 4πr²T`4
= P/ 4πd² × πr² = ⊂ × 4πr²T`4
= ⊂ × 4πR²T`4 / 4πd² = ⊂ × 4πr²T`4
= R²/d²T`4 = 4T`4
√R/dT = (2²)`1/4T
Ts = Te √2d/R