1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help converting kJ/(kg*degC) to Btu/(lbm*degF)

  1. Jun 6, 2017 #1
    1. The problem statement, all variables and given/known data

    Show that 1 kJ/(kg⋅°C) = 0.238846 Btu/(lbm⋅°F) using dimensional analysis and the given conversion factors:

    1 Btu = 1.055056 kJ
    1 kg = 2.2046226 lbm
    T(°F)=1.8⋅T(°C)+32


    2. Relevant equations

    1 Btu / 1.055056 kJ =1
    1 kg / 2.2046226 lbm = 1
    1.8⋅Δ°C / Δ°F=1


    3. The attempt at a solution

    (1 kJ/(kg°C)) ⋅(1 Btu / 1.055056 kJ) ⋅ (1 kg / 2.2046226 lbm) ⋅ (1.8⋅Δ°C / Δ°F) ≈ 0.842661 Btu/(lbm⋅°F)

    I have no idea how this is wrong but it is according any conversion table I've seen.

    Please help, I need to know what I'm doing wrong.

    Thank you
     
  2. jcsd
  3. Jun 6, 2017 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello.

    Check the part where you're converting the temperatures.
     
  4. Jun 6, 2017 #3
    Edit: I think I know what I'm doing wrong but still need help, ready below this post.

    How is it wrong ? I've been staring at it for hours. The change is 1.8 or 9/5 ..

    100 C = 212 F
    0 C = 32 F
    The slope is 9/5 or 1.8 with a y intercept of 32. In the analysis wouldn't this be multiplying by a factor of 1.8 since I'm going from inverse C to Inverse F.. I may be confusing myself with the methodology here idk
     
    Last edited: Jun 6, 2017
  5. Jun 6, 2017 #4
    Sorry for double post

    So I think I understand what's wrong

    The "change in F" and "change in C" is what I'm comparing

    It makes sense that a change of 1.8 F only results in a change in 1 C so I can change my conversion factor... but how do I show this logic rigorously or in math terms? In other words.. how do I show more work stating from the T(F) = 9/5 T(C) + 32 results in 1.8 Δ°F = 1 Δ°C
     
  6. Jun 6, 2017 #5

    TSny

    User Avatar
    Homework Helper
    Gold Member

    This is correct. But this is not what you used in your conversion in the first post.
     
  7. Jun 6, 2017 #6
    Right. Once I replace the conversion factor the answer is correct.

    However I'm still unsure how to take the information
    T(F) = 9/5 T(C) + 32
    and conclude
    1.8 Δ°F = 1 Δ°C

    in a way other than just mental reasoning ... how do I apply math notation to this to show something rigorous? Perhaps I'm concerned out of illusion .
     
  8. Jun 6, 2017 #7

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Consider an arbitrary initial temperature and an arbitrary final temperature. So,

    Tfinal(F) = 9/5 Tfinal(C) + 32

    Tinitial(F) = 9/5 Tinitial(C) + 32

    Subtract the two equations.
     
  9. Jun 6, 2017 #8
    I'm not sure I follow. Won't the 9/5 stay with the T(C) ?
     
  10. Jun 6, 2017 #9

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes. So you will get ΔT(F) = 9/5 ΔT(C). Now interpret this.

    Suppose you consider the case where the temperature change is 1 Co. The interpretation of the equation is that it tells us that this temperature change of 1 Co will be a change on the Fahrenheit scale of 9/5 Fahrenheit degrees.

    The confusion might be coming from the fact that the 9/5 has hidden units. The 9/5 has units of Fo/Co. So, when we consider a temperature change of 1 Co, we have

    ΔT(F) = (9/5 Fo/Co) ⋅ (1Co) = 9/5 Fo.

    So, 1 Co is equivalent to 9/5 Fo.
     
  11. Jun 6, 2017 #10
    The suppressed units is what got me. Makes perfect sense now
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help converting kJ/(kg*degC) to Btu/(lbm*degF)
  1. Converting Btu to J (Replies: 5)

Loading...