Why is enthalpy an extensive property?

Enthalpy (H) is considered an extensive property because it depends on the amount or quantity of substance present in a system. Extensive properties are properties of a system that scale with the size or extent of the system. In other words, as you increase the amount of substance or the size of the system, the value of the extensive property also increases proportionally.

Mathematically, enthalpy is defined as:

H = U + PV

Where:

H is the enthalpy
U is the internal energy of the system
P is the pressure of the system
V is the volume of the system
Both the internal energy (U) and the product of pressure (P) and volume (V) are extensive properties. Since enthalpy incorporates these two extensive properties (U and PV), enthalpy itself becomes an extensive property.

When you have a larger system with more substance, both the internal energy and the product of pressure and volume will be greater, leading to a higher enthalpy value. This is why enthalpy is directly related to the quantity of substance and the size of the system, making it an extensive property.