Question

A college student is working on her physics homework in her dorm room. Her room contains a total of 6.0 X10^26 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 (dorm 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 19min ?

Answer 1

Answer:

$\Delta T =11.904\ K$

Explanation:

given,

total gas molecule , N = 6 x 10²⁶

Power,P = 125 W

Δ t = 19 min = 19 x 60 s

Δ T = ?

Power,

$P = \dfrac{energy}{time}$

$E_n=P\times \Delta t$

$E_n=125\times 19\times 60$

$E_n=142500\ J$

we now,

$E_n = \dfrac{3}{2}Nk_b\Delta T$

$\Delta T = \dfrac{E_n}{\dfrac{3}{2}Nk_b}$

where as, k_b = 1.38 x 10⁻²³ J/K

$\Delta T = \dfrac{142500}{\dfrac{3}{2}\times 6 \times 10^{26}\times 1.38 \times 10^{-23}}$

$\Delta T =11.904\ K$

The increase in temperature is equal to $\Delta T =11.904\ K$