An office heater puts out 2010 Btu (British thermal units) of energy in the form of heat per hour.

Question

An office heater puts out  (British thermal units) of energy in the form of heat per hour. Given that  how many megajoules of energy in the form of heat can be produced per year (365 days) by the heater, assuming continuous operation?

Answer 1

Hello, Emilie,

We are given a value of 2010 BTU/hr for the heater. But the question wants MegaJoules/year. Let's set up some conversion factors that will make this change for us.

We need to go from hours to years, so let's calculate the number of hours in a year:

365 days/yr

24 hr/day

(365 days/yr)*(24 hr/day) = 8760 hr/year

Now we can calculate the BTU/year for the heater:

(2010 BTU/hr)*(8760 hr/year) = 1.761x10⁷ BTU/year

Now we need a conversiuon factor to change BTU to Joules.

I BTU = 1055.1 Joule

I'll rewrite this as: (1055.1 Joule/1 BTU)

Since the top and bottom are equivalent, we can write this also as (1 BTU/1055.1 Joule). Conversion factors are all equivalent to "1" since thwe top and bottom are the same, with the change only in units.

I choose (1055.1 Joule/1 BTU) in this case, since I want to multiply to convert the BTU into Joules:

(1.761x10⁷ BTU/year)*(1055.1 Joule/1 BTU) = 1.858x10¹⁰ Joules/year

I'm glad scientific notation was invented. That's a lot of zeros. (18,580,000,000 Joules/year)

We need to divide by 1000 since we want MegaJoules, not Joules

(1.858x10¹⁰ Joules/year)/(1000Joules/MegaJoule) = 1.858x10⁷ MegaJoules/year

[ Or we could have multiplied by the inverse of (1000 Joules/MegaJoule), which would be (1 MegaJoule/1000 Joules)]

(1.858x10¹⁰ Joules/year)*(1 MegaJoule/1000 Joules) = 1.858x10⁷ MegaJoules/year

Bob