Solving Room Temperature Issues - Help!

[a13x]

room temperatures, please help!

Homework Statement

A room is initially at the outdoor temperature of 25C. Now a large fan that consumes 200W of electricity when running is turned on. The heat transfer rate between the room and the outdoor air is given as Q = UA(Ti - To) where U = 6 W/m^2^.oC is the overall heat transfer coefficient, A = 30 m^2 is the exposed surface area of the room, and Ti and To are the indoor and outdoor temperatures, respectively. Determine the indoor air temperature when steady operating conditions are established.

Homework Equations

Q = UA(Ti - To)

The Attempt at a Solution

Not really sure where to start with this problem.

 

[Doc Al]

Hint: What happens to the 200 W of power "consumed" by the fan?

 

[P111ltl]

I take it that only a percentage of the energy consumed is given off as heat the rest is transferred into other energy forms obeying the energy cannot be creasted or destroyed rule just transformed from one source to another.

 

[a13x]

I know some of the energy used will be converted to heat and noise but can't seem to find an equation to work it out.

I think the indoor temperature will be the initial 25^oC plus however much heat is given off by the fan. Not sure if I am correct in this assumption or not.

 

[mgb_phys]

You have to assume that all the 200W is put out as heat.
You probably also have to assume that this heat all goes into the room, otherwise there would be no point in telling you the value!

 

[a13x]

Got it now. Energy in and out have to be equal. With the energy in being 200J, the same has to be said or energy out. Ti = To = 200.

Just have to convert the equation so Ti is the unknown.

Thanks for the help guys

 

[mgb_phys]

Yes, but be careful, Ti/To are the temperatures not the energy.