Question

A college student is working on her physics homework in her dorm room. Her room contains a total of 6.0 x 10^26 gas molecules. As she works, her body is converting chemical energy into thermal energy at a rate of 125 W. If her dorm room were an isolated system (darm rooms can certainly feel like that) and if all of this thermal energy were transferred to the air in the room, by how much would the temperature increase in 6.0 min? Express your answer using two significant figures

Answer 1

Answer:

Temperature, T = 3.62 kelvin

Explanation:

It is given that,

Total number of gas molecules, $N=6\times 10^{26}$

Her body is converting chemical energy into thermal energy at a rate of 125 W, P = 125 W

Time taken, t = 6 min = 360 s

Energy of a gas molecules is given by :

$\Delta E =\dfrac{3}{2}NkT$

$T=\dfrac{2E}{3Nk}$, k is Boltzmann constant

$T=\dfrac{2\times P\times t}{3Nk}$

$T=\dfrac{2\times 125\times 360}{3\times 6\times 10^{26}\times 1.38\times 10^{-23}}$

T = 3.62 K

So, the temperature increases by 3.62 kelvin. Hence, this is the required solution.