A college student is working on her physics homework in her dorm room. Her room

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 12 min? HELP please I cant seem to get the correct answer! (in degrees Celsius)

Explanation / Answer

We can assume that the air consists of diatomic molecules only (98% is O2 and N2, so our approximation is fair)
The increase in energy = nCv dT
Cv is the specific heat capacity of diatomic molecules,
Cv = 5/2 R = 20.8 J/mol K
n is the number of moles = Total number of gas molecules / Avagadro number
n = 6.0 X1026 / 6.02214129 x 10 23. = 103 mol.
Increase in energy = 103 x 20.8 J/mol K x dT

Power = 125 W
In one second, 125 J is produced
For 12 minutes, 125 x 12 x 60 J = 90000 J is produced

103 x 20.8 J/mol K x dT = 90000 J
dT = 90/20.8 = 4.32 degrees = 4.32 K (Since it is change in temperature)

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