# Zeroth Law MIT Courseware

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1. Jan 19, 2016

### Aniket1

I was studying zeroth law from MIT Courseware (http://ocw.mit.edu/courses/physics/...-fall-2013/lecture-notes/MIT8_333F13_Lec1.pdf). On page 2, it is mentioned that equation I.4 can be simplified using equation I.5 by cancelling the co-ordinates of C. Could someone guide me justify this fact? I tried working it out by assuming functions and I could construct functions where equation I.4 and equation I.5 are satisfied but it is not possible to cancel C. Am I missing something?

2. Jan 20, 2016

### Useful nucleus

Equation I.4 does not contain C1. Now let' eliminate C2. Differentiate I.4 with respect to A1, then you will get

F#AC(A1,A2,...,C2,...)=0

But then you can write this equation as C2=GAC(A1,A2,...,C3,C4,...).

Similarly, differentiate I.4 with respect to B1. Then you will get
F#BC(B1,B2,...,C2,....)=0

But again you can write it as C2=GBC(B1,B2,...,C3,C4,...).

Since there is equilibrium then,
GBC(B1,B2,...,C3,C4,...) = GAC(A1,A2,...,C3,C4,...).

Thus, you eliminated C2. Repeat the procedure unti you eliminate all C's . Then you will end up with
θA(A1,A2,....)=θB(B1,B2,...).

3. Jan 20, 2016

### Useful nucleus

4. Feb 12, 2016