Question

The rates of heat radiation from two patches of skin each of area $A$, on a patient's chest differ by $2\%$. If the patch of the lower temp is at $300K$ and emissivity of both the patches is assumed to be unity, the temperature of the other patch would be

• A. 306K
• B. 312K
• C. 308.5K
• D. 301.5K

Answer 1

The correct option is D 301.5K

Here it is given that temperature of second skin will vary by $2$%
let, the initial length be $100$% and after variation it will be $\left(100-2\right)${%}
So, from heat released by radiation is given as $Q=\sigma A{T}^4$
So, $\frac{X_1}{X_2}=\frac{T_2^4}{T_1^4}$
Therefore,$\frac{100}{98}=\frac{T_2^4}{{300}^4}$
$T_2=301.5K$