136. A spherical black body with a radius of 12 cmradiates 450 watt power at 500 K. If the radius werehalved and the temperature doubled, the powerradiated in watt would be
(1) 225 (2) 450
(3) 1000 (4) 1800
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The power radiated in watt would be :
• Given : Radius R1 = 12cm, Rate of radiation = 450, Temperature, T1=500K
• Also given R2 = 1/2R1 and T2 = 2T1
• We know that, Rate of power loss is given as
• r ∝ R^2×T^4
r1 / r2 = R1^2×T1^4 / R2^2×T2^4
= 4 × 1/16 = 1/4
450/r2 = 1/4
• r2 = 1800 watt
Answered by
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The power radiated in watt would be 1800 Watt.
Explanation:
Given data:
- Radius R1 = 12 cm
- Rate of radiation = 450 Watt
- Temperature, T1 = 500 K
Also given R2 = 1 / 2R1 and T2 = 2T1
We know that:
Rate of power loss is given as
r ∝ R^2×T^4
r1 / r2 = R1^2 × T1^4 / R2^2 × T2^4
= 4 × 1/16 = 1/4
450/r2 = 1/4
r2 = 1800 watt
Thus the power radiated in watt would be 1800 Watt.
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