Two identical metal balls at temperature `200^(@)C` and `400^(@)C` kept in air at `27^(@)C`. The ratio of net heat loss by these bodies is

Options

A. ` ( 1 ) /( 4 ) `
B. ` ( 1 ) /( 2 ) `
C. ` ( 1 )/( 16 ) `
D. ` ( ( 473 ) ^ 4 - (300) ^ 4 ) /( (673 ) ^ 4 - ( 300) ^ 4 ) `

Answer

D

Explanation

If temperature of surrounding is considered, then net loss of energy of a body by radiation
` Q = Ae sigma ( T^ 4 - T _ 0 ^ 4 ) t `
` rArr Q prop ( T ^ 4 - T_ 0 ^ 4 ) rArr ( Q _ 1 ) /( Q _ 2 ) = ( T _ 1^4 - T _ 0 ^ 4 ) /( T _ 2 ^ 4 - T_0 ^ 4 ) `
` rArr ( Q _ 1 ) /( Q _ 2 ) = ((273 + 200 ) ^ 4 - (273 + 27 ) ^ 4 ) /( ( 273 + 400) ^ 4 - ( 273+ 27 ) ^ 4 ) `
` = (( 473 ) ^4 - (300) ^ 4 ) /( (673)^4 - (300) ^ 4 ) `