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Question: Two identical metal balls at temperature 200<sup>0C</sup> and 400<sup>0C</sup> kept in air at 27<sup...

Two identical metal balls at temperature 2000C and 4000C kept in air at 270C. The ratio of net heat loss by these bodies is

A

1/ 4

B

1/ 2

C

1/ 16

D

4734−30046734−3004\frac{473^{4} - 300^{4}}{673^{4} - 300^{4}}

Answer

4734−30046734−3004\frac{473^{4} - 300^{4}}{673^{4} - 300^{4}}

Explanation

Solution

Emissive power of a body (T) in a surrounding (T0),

E=σ(T4−T04)E = \sigma(T^{4} - T_{0}^{4}) or Q∝(T14−T04)Q \propto (T_{1}^{4} - T_{0}^{4})

⇒Q1Q2=(T14−T04)(T24−T04)=(473)4−(300)4(673)4−(300)4\frac{Q_{1}}{Q_{2}} = \frac{(T_{1}^{4} - T_{0}^{4})}{(T_{2}^{4} - T_{0}^{4})} = \frac{(473)^{4} - (300)^{4}}{(673)^{4} - (300)^{4}}.