Thread: help substituting one formula into another

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!

Originally Posted by dexev

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!

Here's a rundown for you.

Step by step.




Now, v is an independent variable here, so no T dependence.



Putting this into the U equation:


Upon simplifying (Hah!) you get the book's answer.

-Dan