Question

If x and y are two intensive variables then-
$\mathrm A.\;\mathrm{xy}\;\mathrm{is}\;\mathrm{intensive}\;\mathrm{variable}\;\\\mathrm B.\;\dfrac{\mathrm x}{\mathrm y}\;\mathrm{is}\;\mathrm{intensive}\;\mathrm{variable}\\\mathrm C.\;\;\mathrm x+\mathrm y\;\mathrm{is}\;\mathrm{intensive}\;\mathrm{variable}\\\mathrm D.\;\dfrac{\mathrm{dx}}{\mathrm{dy}}\;\mathrm{is}\;\mathrm{extensive}\;\mathrm{property}$

Answer 1

Hint: Intensive properties are the ones which are independent of the mass or amount. On the other hand, extensive properties are the ones which are dependent on the mass and amount. We can use an example of PV=nRT, where pressure(P) and temperature(T) are intensive and volume(V) and moles(n) are extensive. Then we can check each option one by one.

Complete step-by-step answer:
Let us first consider an example and try to understand this better.
PV=nRT
Here, Pressure(P) and Temperature(T) are intensive and Volume(V) and moles(n) are extensive.
We can satisfy the options using this and check if they are correct or not.

x and y are two intensive variables, hence it is clear that the product of these two will also be intensive. Also, the ratio of two intensive properties is also intensive. When we consider the ratio of change in two intensive properties, the resulting property is intensive.

In option A, we have a product of two intrinsic properties, that is, both of them are mass independent hence the product should also be mass independent, that is, intensive variable.

In option B, we have a ratio of two intensive variables, hence their result should be intensive.

In option C, the sum of two intensive variables will also be intensive, because we can add quantities with the same dimensions, and the sum will also have the same dimensions.

In option D, the ratio of change in two intensive variables is given. We know that the change in intensive variable will also be an intensive variable. So, their ratio will also be intensive.

The correct options are A, B and C.

Note: In such questions, always verify the options using a suitable example. This way we can solve the problem even without knowing the correct answer. Also, we should always check each and every option carefully as more than one option may be correct.