If the temperature of hot black body is raised by 5%, rate of heat energy radiated would be increased by how much percentage ?

Options

A. 0.12
B. 0.22
C. 0.32
D. 0.42

Answer

B

Explanation

According to Stefan.s law, the rate of energy radiated by a black body at absolute temperature T is
`E= A sigmaT^(4)`
When the temperature of the body is raised by 5%, its new tempeature becomes
`T. = T + (5)/(100) T = (21)/(20)T :. (E.)/(E ) = ((T.)/(T))^(4) = ((21)/(20))^(4)= (1.05)^(4)`
% increase in rate of heat energy `= (E.-E)/(E ) xx 100`%
`=((E.)/(E )-1) xx 100% = [(1.05)^(4)-1] xx 100% = 22%`