Why you need a integration constant

[Vdslaur]

Can someone help me with this integration?

Don't understand why you need a integrationconstant.

I would do : RTlnC = U but this isn't correct, you have to put + cte

Why?

 

[oli4]

Hallo Vdslaur
The derivative of a Cte is 0
When you integrate something, the result is always true up to a cte, since if you derive you will get the same answer back for any cte.
That tells you the potential energy '0' is undefined, it's arbitrary, all that matters are its variations. in general you want to set it 0 at infinity.

 

[Vdslaur]

Hallo Vdslaur
The derivative of a Cte is 0
When you integrate something, the result is always true up to a cte, since if you derive you will get the same answer back for any cte.
That tells you the potential energy '0' is undefined, it's arbitrary, all that matters are its variations. in general you want to set it 0 at infinity.

I know that you integrate the U but

for exmple : the integration of dx = x + cte

But here the integration gives you : RTlnC +cte

So : dU = d(RTlnC)

Solution after integration of dU = U
Solution after integration of d(RTlnC) = RTlnC + cte

This is right no?

d(RTlnC) = RT d(lnC)

And d(lnC) is the same as dx , so x + cte --> here : lnC + cte

yes, I get it!