Dimensional Analysis? Involving Temperature

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SUMMARY

The discussion focuses on converting BTU/(ft*hr*F) to W/(m*C) using dimensional analysis. The correct conversion factor is established as 1 BTU/(ft*hr*F) = 1.73 W/(m*C). The conversion process involves breaking it down into steps: converting BTUs to Joules, converting Joules per hour to Watts, adjusting for feet to meters, and applying the ratio of temperature differences between Fahrenheit and Celsius (1.8 F/C). The key takeaway is that the offset in temperature scales does not affect the ratio when dealing with temperature differences.

PREREQUISITES
  • Understanding of dimensional analysis
  • Knowledge of unit conversions (BTU to Joules, feet to meters)
  • Familiarity with temperature scales (Fahrenheit and Celsius)
  • Basic principles of thermodynamics and heat transfer
NEXT STEPS
  • Study the principles of dimensional analysis in physics
  • Learn about unit conversion techniques for energy and temperature
  • Explore the relationship between different temperature scales
  • Investigate the applications of heat transfer calculations in engineering
USEFUL FOR

Students in physics or engineering, professionals in thermodynamics, and anyone involved in heat transfer calculations will benefit from this discussion.

delsloww88
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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.
 
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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
 
Thanks for clearing that up the 1.8 F/C was where I was going wrong.
 

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