- #1
mSSM
- 31
- 1
The following actually comes from Landau's 3rd Edit. Statistical Physics Part 1, Paragraph on Adiabatic Processes, Page 39.
I have the following two equations, where \lambda=\lambda(t). I am not so sure about S (which is somewhat my problem):
\frac{\mathrm{d}S}{\mathrm{d}t} = \left( \frac{\mathrm{d}\lambda}{\mathrm{d}t} \right)^2
Which is supposed to mean:
\frac{\mathrm{d}S}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}
Now, I thought that what is essentially being done there is multiplying the first equation such that we get:
\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}
But if I now assume that:
\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}S}{\mathrm{d}\lambda}
doesn't that in turn mean that t is a function of \lambda? Mathematically this seams sounds (to me), but physically this does not make so much sense, if t is the time.
I have the following two equations, where \lambda=\lambda(t). I am not so sure about S (which is somewhat my problem):
\frac{\mathrm{d}S}{\mathrm{d}t} = \left( \frac{\mathrm{d}\lambda}{\mathrm{d}t} \right)^2
Which is supposed to mean:
\frac{\mathrm{d}S}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}
Now, I thought that what is essentially being done there is multiplying the first equation such that we get:
\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}\lambda}{\mathrm{d}t}
But if I now assume that:
\frac{\mathrm{d}S}{\mathrm{d}t}\frac{\mathrm{d}t}{\mathrm{d}\lambda} = \frac{\mathrm{d}S}{\mathrm{d}\lambda}
doesn't that in turn mean that t is a function of \lambda? Mathematically this seams sounds (to me), but physically this does not make so much sense, if t is the time.
