Write the two kinds of thermodynamic state variables and explain them.

(N/A) There are two types of thermodynamic state variables:
$(1)$ Extensive variables and $(2)$ Intensive variables.
Extensive variables depend on the size or the amount of matter present in the system. Examples include internal energy $U$,volume $V$,total mass $M$,and entropy $S$.
Intensive variables are independent of the size or the amount of matter present in the system. Examples include pressure $P$,temperature $T$,and density $\rho$.
To distinguish between them,consider a system in equilibrium and imagine dividing it into two equal parts. The variables that remain unchanged for each part are intensive,while those whose values are halved are extensive.
It is useful to check the consistency of thermodynamic equations using this classification. For example,in the equation $\Delta Q = \Delta U + P \Delta V$,all terms are extensive. While pressure $P$ is intensive and $\Delta V$ is extensive,their product $P \Delta V$ is an extensive variable.