Question

A student is trying to decide what to wear. His bedroom is at ${20^0}C$ His skin temperature is ${35^0}C$ The area of his exposed skin is $1.50\,{m^2}$ People all over the world have skin that is dark in the infrared, with emissivity about $0.900$ Find the net energy transfer from his body by radiation in $10.0\min $.

Answer 1

Hint: In order to solve this question, we will first calculate the power transferred from the skin of the student using the general formula of power emitted in case of black body radiation and then we will calculate the energy emitted by the body of student for given period of time.

Formula used:
Power emitted by a body with a temperature difference from surface area is calculated as
$P = \sigma Ae({T^4} - {T_0}^4)$
where, $\sigma = 5.67 \times {10^{ - 8}}W{m^{ - 2}}{K^{ - 4}}$ known as Stefan constant, $A$ is area which is given in question as $A = 1.50{m^2}$, $e = 0.900$ known as emissivity constant, $T$ is the temperature of the body given in question as $T = {35^0}C$ and ${T_0} = {20^0}C$ the temperature of surrounding of the body.

Complete answer:
Now to calculate power emitted by the body of student, using the formula $P = \sigma Ae({T^4} - {T_0}^4)$ on putting the value we get,
$P = 5.67 \times {10^{ - 8}} \times 1.50 \times 0.900({T^4} - {T_0}^4)$
converting temperature from Celsius to kelvin we have,
$T = 35 + 273 = 308K$
$\Rightarrow {T_0} = 20 + 273 = 293K$
Now,
$P = 5.67 \times {10^{ - 8}} \times 1.50 \times 0.900({(308)^4} - {(293)^4})$
$\Rightarrow P = 125\,W$
Now, in order to calculate the energy emitted by body in time of $t = 10.0\min = 600\sec $ we know that,
$E = P \times t$
so we have,
$E = 125 \times 600J$
$\therefore E = 72\,KJ$

Hence, the net energy transferred in period of ten minutes by the body of student is $E = 72\,KJ$.

Note: It should be remembered that, the basic conversion rule of Celsius scale to kelvin scale is given as $K{ = ^0}C + 273$ and Kilo-Joule is a unit of energy written as KJ and its value is $1KJ = 1000J$ also, In the infrared region of light a normal person shines much brighter than a hundred-watt light bulb.