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If x and y are two arbitrary extensive thermodynamic variables, which of the following is an intensive variable?

1. (x + y) is an intensive variable
2. x/y is an intensive variable
3. (x - y) is an intensive variable
4. x * y is an intensive variable

Correct answer: x/y is an intensive variable

Solution

An extensive variable scales proportionally with the amount of substance (e.g., volume, internal energy). When system size is scaled by factor k, extensive variables become k*x and k*y. The ratio x/y becomes (k*x)/(k*y) = x/y, which is unchanged. Hence x/y is intensive. The sum (x+y) becomes k*(x+y) (extensive), the difference (x-y) is also extensive, and the product x*y becomes k²*x*y (not a standard thermodynamic quantity and certainly not intensive).

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