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

Temperature, T = 3.62 kelvin

Step-by-step explanation:

It is given that,

Total number of gas molecules,
`N=6* 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 =(3)/(2)NkT`

`T=(2E)/(3Nk)`, k is Boltzmann constant

`T=(2* P* t)/(3Nk)`

`T=(2* 125* 360)/(3* 6* 10^(26)* 1.38* 10^(-23))`

T = 3.62 K

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