What is the difference between specific internal energy and specific enthalpy in first law of Thermodyanamics and when should i use which?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
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Chapter8: Natural Convection
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Problem 8.3P
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What is the difference between specific internal energy and specific enthalpy in first law of Thermodyanamics and when should i use which?

From what i understand so far for constant pressure process, we use q-w=h2-h1 and constant volume process, we use q-w = u2-u1. But this isnt the answer i am looking for. 

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