I am studying David M. Himmelblau's book on material and energy balances, and I'm finding it challenging to intuitively grasp the difference between extensive and intensive properties, particularly regarding their ability to be summed.

I understand that:

• Extensive properties: These are properties whose values are the sum of the values of the subsystems that make up the entire system (e.g., mass and volume).
• Intensive properties: These are properties whose values are not additive and do not vary with the amount of material in the system (e.g., temperature and pressure). These properties describe the state of the system at a given moment.

My questions are:

• How can a student intuitively understand why certain intensive properties, like temperature, are not summed when combining subsystems? For example, if I have two blocks of metal, one at 50°C and another at 100°C, the temperature of the combined system is not 150°C but will equilibrate to an intermediate value. This doesn't seem intuitive at first.
• What exactly does it mean that intensive properties "describe states"? Are temperature and pressure the only variables used to describe the state of a system, or are there other intensive properties that also serve this function?

I would appreciate explanations or examples that can help clarify these concepts in a more intuitive way for students, so they can understand why some properties can be summed and others cannot, and how this relates to the description of the state of a thermodynamic system.