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

Concepts and reason

The concept used to solve this problem is internal energy of monoatomic gas.

First use the relation between energy and time to calculate the power.

Finally use the relation between internal energy, number of molecules, Boltzmann constant to calculate the change in temperature.

Fundamentals

Expression for the energy is,

Here, is the change in energy, P is the power, and is the change in time.

Expression for the energy of the monoatomic gas is,

Here, is the change in temperature, is the Boltzmann constant, and N is the number of molecules.

Expression for the energy is,

Substitute for P and for in the equation .

Rearrange the equation to get the change in temperature.

Substitute for , for , and for N in the equation .

Ans:

The change in temperature is.