Question

If x and y are arbitrary intensive variables, then:
(A)- xy is an intensive variable
(B)- x/y is an intensive variable
(C)- x+y is an intensive variable
(D)- dx/dy is an intensive variable

Answer 1

Hint: A physical property of a system that does not depend on the system size or the amount of material in a system is known as an intensive property. By contrast, a physical property of a system that does not depend on the system size or the amount of material in a system is known as extensive properties.

Complete Step by step solution:
-The behaviour of a system depends on the interaction of various forms and types with or without mass transfer across the boundary, and such behaviour or characteristics of a system are called the properties of a system.
-Eight properties describe the behaviour of a system: pressure, temperature, volume, entropy, internal energy, enthalpy, Gibb’s function, and Helmholtz function. Among these properties, pressure, temperature, and volume are measurable properties and they are known as Physical properties or Macroscopic properties. Other properties cannot be measured directly, hence are known as Derived properties.
-The thermodynamic properties can be categorized into two general classes- intensive properties; and extensive properties.
-The product of two intensive variables is always intensive, hence option A is correct.
-The ratio of two intensive variables is always intensive, hence option B is also correct.
-The addition of two intensive variables is always intensive, which is against the statement mentioned in option C, hence option C is incorrect.
-dx/dy can also be written as $\dfrac{\Delta x}{\Delta y}$which is simply a ratio, hence it is also an intensive property.

Therefore, the correct answers are options A, B, and D.

Note: Extensive properties are symbolized by capital (uppercase) letters, for example, V (volume), KE (kinetic energy), PE (potential energy). Intensive properties are symbolized by small (lowercase) letters, for example, v (specific volume), ke (specific kinetic energy), h (specific enthalpy), etc. However, there are some exceptions for symbols, like temperature is an intensive but symbolized by ‘T’ rather than lowercase letters, mass and number of moles being extensive properties are symbolized by ‘m’ and ‘n’ rather than uppercase letters.