Question

If The total solar energy received by surface of earth in a day is 15.6 ×10^18 KJ , find the radius of earth

Answer 1

It has given that total solar energy received by the surface of the earth in a day is 15.6 × 10^18 kJ

To find : The radius of the earth.

solution : experimentally, intensity of sunlight on the earth's surface , I = 1360 W/m²

power = total energy/time taken

= 15.6 × 10^18 × 10³ J/(1 day )

= (15.6 × 10²¹ J)/(24 × 3600 s)

= (15.6 × 10²¹)/(86400) W

= 0.0001805 × 10²¹ W

= 1.805 × 10^17 W

now using formula of intensity, I = P/A

⇒I = P/πR²

⇒R² = P/πI

here, P = 1.805 × 10^17 W , l = 1360 W/m²

so, R² = (1.805 × 10^17)/(3.14 × 1360)

= 0.000423 × 10^17

= 4.23 × 10¹³

= 40.23 × 10¹² m²

R = √(40.23) × 10⁶ m = 6.3427 × 10⁶ m

= 6342.7 km

Therefore the radius of the earth is 6342.7 km (approximately)