First of all apologies if this is in the wrong section, I really wasn't sure where to put it. I'm a physics student in my 2nd year at university and came across the following in a text book:
Note that all derivatives are partial
(1) U=(1/C)*(P - T*(dP/dT))
(2) P*v = RT(1+B/v)
Substitute (2) into (1) gives:
U= (-1/C) * ((RT^2)/v^2) * (dB/dT)
The book just gives the result and misses out all the mathematical steps and when I try it myself I just can't get that result.
from (2) P= ((RT)/v) + ((RTB)/v^2)
dp/dt = R/v + (RB)/v^2
Substitute in gives:
U = (1/c) * [ { ((RT)/v) + ((RTB)/v^2) } - { T*(R/v + (RB)/v^2) } ]
Which just equals zero?
I'm sure I must be doing something obvious wrong, but can't see it.. any help would be appreciated!