Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density $$(\rho)$$ are intensive variables. (C) Volume (V), temperature (T) and density $$(\rho)$$ are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

Concept: Extensive vs intensive thermodynamic variables.

Definitions:

Extensive variables depend on the size/amount of the system (they scale with the quantity of matter). Examples: internal energy, volume, mass, enthalpy, entropy.

Intensive variables are independent of the size of the system. Examples: pressure, temperature, density.

Evaluating each statement:

(A) Internal energy, volume (V), and mass (M) are extensive variables.

All three depend on the amount of matter. Statement A is correct.

(B) Pressure (P), temperature (T), and density ($$\rho$$) are intensive variables.

None of these depend on the system size. Statement B is correct.

(C) Volume (V), temperature (T), and density ($$\rho$$) are intensive variables.

Volume is an extensive variable (it doubles when the system size doubles). Statement C is incorrect.

(D) Mass (M), temperature (T), and internal energy are extensive variables.

Temperature is an intensive variable. Statement D is incorrect.

Correct statements: (A) and (B) only, which corresponds to Option 4.