Question

Two identical bodies A and B are heated to temperature 400K and 350K respectively. The room temperature is 27°C. Compare their rate of loss of heat.

Solution

Given that,
$Temperature space of space first space body space straight A comma space straight T subscript 1 space equals space 400 straight K Temperature space of space body space straight B comma space straight T subscript 2 space equals space 350 straight K$
$Initial space temperature comma straight T subscript straight o space equals space 27 degree straight C space equals space 300 straight K$
According to Stefan's law,
$straight E proportional to left parenthesis straight T to the power of 4 minus straight T subscript straight o to the power of 4 right parenthesis$
∴ $straight E subscript 1 over straight E subscript 2 equals fraction numerator straight T subscript 1 to the power of 4 minus straight T subscript straight o to the power of 4 over denominator straight T subscript 2 to the power of 4 minus straight T subscript straight o to the power of 4 end fraction$
$equals fraction numerator left parenthesis 400 right parenthesis to the power of 4 minus left parenthesis 300 right parenthesis to the power of 4 over denominator left parenthesis 350 right parenthesis to the power of 4 minus left parenthesis 300 right parenthesis to the power of 4 end fraction equals 2.326$
This is the ratio of loss of heat.