Question

For a block body temperature ${727}^{o}C,$ its rate of energy loss is $20watt$ and temperature of surrounding is ${227}^{o}C.$ If temperature of black body is changed to ${1227}^{o}C$ then its rate of energy loss will be:

• A. $320W$
• B. $\frac{304}{3}W$
• C. $240W$
• D. $120W$

Answer 1

The correct option is A $320W$

It is given that,

Temperature of surrounding

$T_0={227}^{0}C=500K$

$T_1={727}^{0}C=1000K$

$T_2={1227}^{0}C=1500K$

$E_1=20Watt$

$E_2=?$

According to Stefn boltzmann law:

$E=\sigma T^4$

Or

$E_1=\sigma (T_1-T_0{)}^4$

$E_2=\sigma (T_2-T_0{)}^4$

Taking ratios of above equations:

For $E_1=20Watt$

$\frac{20}{E_2}={\left(\frac{500}{1000}\right)}^4$

$\frac{20}{E_2}=\left(\frac{1}{16}\right)$

$E_2=320Watt$