Heating a house, energy loss to surroundings

[jbphysics]

Tried to figure this out for a friend but couldn't quite get it. Here is the problem.

For 3 hours one winter afternoon, outside temp is 0* C. A house is heated and kept at 20* C with the expenditure of 45 kwh. What was the average energy leakes in joules per second through the walls of the house to the environment?

I'm sure this is a simple playing with numbers, but without the right answer i cannot be sure of my method. Help appreciated!

Thanks

 

[HallsofIvy]

You could certainly calculate that the energy expenditure is 45 kwh*3 h= 135 kw. If the temperature in the house was originally 30 degrees and you used that energy to keep the house at that same temperature (i.e. did NOT change the total energy in the house) isn't it obvious that all of that 135 kw went outside?

 

[phlegmy]

this sound like homework to me?
but on a more serious note
expending 45kwh is not spending 45kw/h its expending 15kw for 3hrs
if you know your units the answer is right in fromt of you

 

[jbphysics]

the way I looked at it...
If no energy went into the heating system of the house to maintain that temperature of 20* C, the house would surely decrease in temperature since the surroundings are colder. I was thinking all of the 45kwh went into the houses heating system and some of the heat was lost due to the colder surroundings and a house that isn't perfectly insulated.

Is the wording "with the expenditure of 45 kwh" saying that's what was wasted, and it's simply asking me to find an average rate? The answer to this problem with numbers

2 hrs
47 kwh
is 23500 watts which goes along with phlegmy's response.

 

[phlegmy]

if you pump energy into [from any source] a house it must go somewhere!

1> it can cause the house to heat up OR
2> it can cause the house to move OR
3> it can cuase some chemical change within the house OR
4> it can leak out of the house.

if you pump an amount of energy "x" into a house and it doesn't heat up or move etc
then an amount of energy equal to "x" has leaked out of the house.

so if your heating system is using 10j/s and the house aint getting any hotter or colder
then 10j/s is leaking out somewhere

if your house gets hotter, less than 10j/s are leaking
if your house gets colder, more than 10j/s are leaking

if you then stop pumping energy into the house, it will continue to leak energy out, until it reaches the outside temprature, then it'll stop..

a much harder question would involve heating a house up from cold and maintaining it at a temprature, you would need much more information for such a problem, such as the size and material of the house, how much surface area is brick, how much is windows, and the thermal conductivities of each, etc etc.

you question appears much more simple.
if it uses 47kwh over 2hrs and the temp doesn't change then
23.5kw are leaking from the house

if it uses 45kwh over 3 hrs and the temp don't change then
15kw are leaking from the house

 

[clutch12]

so for a question like this are we converting kw to watts and then multiplying it by 60 secs?

 

[Redbelly98]

No, we are dividing energy by the time to get the power. Then kW must be converted to W, since the problem asks for the answer in J/s units.

 

[clutch12]

oh ok thanks for the help