Question

The rates of heat radiation from two patches of skin each of area $S$, on a patients chest differ by $2\%$. If the patch of the lower temperature is at $300K$ and the emissivity of both the patches are assumed to be unity. The temperature of the other patch is:

• A. $301.5K$
• B. $601.5K$
• C. $103.5K$
• D. $106.5K$

Answer 1

The correct option is A $301.5K$

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, $\frac{100}{98}=\frac{T_2^4}{{300}^4}$
$T_2=301.5K$