# Extensive quantity

1. Feb 4, 2008

### ehrenfest

[SOLVED] extensive quantity

1. The problem statement, all variables and given/known data
My teacher said that E=E(S,V,N) implies that c E = E(cS,cV,cN) where c is some constant. The justification was that E is an extensive parameter. I know what an extensive parameter is (proportional to N), but I do not see how that relation follows.

2. Relevant equations

3. The attempt at a solution

2. Feb 5, 2008

### Mapes

1. E, S, V, and N are extensive quantities.
2. You have a system with a certain S, V, and N, and you calculate the energy E.
3. I replace the system with one twice as big.
4. You can either double S, V, and N and recalculate or just double E, right? This statement is identical to your equation.

3. Dec 22, 2011

### Zeppos10

Re: [SOLVED] extensive quantity

the proper definition of an extensive quantity is: if there is a system with extensive quanty X' and another system with X" then the two systems together has property X, with X=X'+X". (the property is additive). This is independent of the existence of a function X(a,b,c) where a b and c are also extensive quantities. For example take the internal energy of systems consisting of mono-atomic ideal gases with for helium U'=n'(3/2)RT' and for neon U"=n"(3/2)RT". (Hence U=U(n,T)). Now if we take the systems together U=U'+U" and n=n'+n", independent of the actual values of T'and T". (and we do not need the constant c)
U (=E) is and extensive quantity independent from the suggested function, that is actually non-existent for most systems.