# Dimensional Analysis? Involving Temperature

1. Sep 19, 2015

### delsloww88

I was trying to convert a quantity in BTU/(ft*hr*F) to W/(m*C) and I can do it just fine by using a conversion factor from a table online, but what I want to know is how to come up with that conversion factor.

The conversion factor I looked up and have been using is 1 BTU/(ft*hr*F) = 1.73 W/(m*C). I tried to get this using dimensional analysis but it does not work. I think the problem is going from F to C because they do not have the same zero point. If that is the problem and I can't solve this with dimensional analysis how could I do it.

2. Sep 19, 2015

### leright

Break it up into pieces. First convert BTUs to Joules. Then convert Joules/Hr to Watts (hint: divide by 3600 seconds/Hr). That gives you W/(ft*F). Then multiply by the number of feet/meter. The multiply by the ratio of deltaF/deltaC = 1.8. The only thing that should matter is the ratio of the deltas of the degree C and degree F. The offset shouldn't matter here since you aren't making absolute temperature measurements. You're only concerned with the number of a quantity per unit temperature.

So it looks something like this: (1055.056 J/BTU)*(1/3600 Hr/s)*(3.28084 ft/meter)*(1.8 F/C) = 1.73

3. Sep 19, 2015

### delsloww88

Thanks for clearing that up the 1.8 F/C was where I was going wrong.