What will be the increment in heat energy radiated when the temperature of hot body is raised by `5%` ?

Options

A. `12%`
B. `22%`
C. `32%`
D. `42%`

Answer

B

Explanation

According to Stefan-Boltzmann.s law,
`EpropT^(4)`
`:.(E_(2))/(E_(1))=((T_(2))/(T_(1)))^(4)`
`:.(E_(2))/(E_(1))=((T_(1)+0.05T_(1))/(T_(1)))^(4)`
`:.(E_(2))/(E_(1))=((1.05T_(1))/(T_(1)))^(4)`
Increase in temp. is
`5%`. So, `T_(2)=(5)/(100)T_(1)+T_(1)`
`:.T_(2)=0.05T_(1)+T_(1)`
`:.(E_(2))/(E_(1))=(1.05)^(4)`
`:.(E_(2)-E_(1))/(E_(1))xx100=(1.2155-1)/(1)xx100`
`=0.2155xx100`
`=21.55%`
`~~22%`