Basic of Thermodynamics and Zeroth Law Questions in English

(C) Thermal equilibrium is a state in which two or more bodies in thermal contact do not exchange net heat energy.
According to the Zeroth Law of Thermodynamics,two systems are in thermal equilibrium if and only if they are at the same temperature.
Therefore,the correct condition for thermal equilibrium is that the gases must have the same temperature.

(C) Extensive variables are those that depend on the size or the amount of matter present in the system. Examples include internal energy,volume,and mass.
Intensive variables are those that are independent of the size or the amount of matter present in the system. Examples include pressure,temperature,and density.
Evaluating the statements:
$(A)$ Internal energy,volume,and mass are indeed extensive variables. This statement is correct.
$(B)$ Pressure,temperature,and density are indeed intensive variables. This statement is correct.
$(C)$ Volume is extensive,while temperature and density are intensive. This statement is incorrect.
$(D)$ Temperature is intensive,while mass and internal energy are extensive. This statement is incorrect.
Therefore,statements $(A)$ and $(B)$ are correct.

(A) Thermodynamic coordinates are the state variables that define the state of a thermodynamic system,such as pressure $(p)$,volume $(V)$,and temperature $(T)$.
$R$ is the universal gas constant,which is a fundamental constant of nature and not a variable that describes the state of a specific system.
Therefore,the gas constant $(R)$ is not a thermodynamic coordinate.

(B) The zeroth law of thermodynamics states that if two systems are each in thermal equilibrium with a third system,then they are in thermal equilibrium with each other.
Thermal equilibrium is defined as the state in which two systems in contact with each other do not exchange any net heat.
This condition is satisfied when both systems have the same temperature.
Therefore,the physical quantity that remains the same for two bodies in thermal equilibrium is temperature.

(C) Thermodynamic state variables are properties that depend only on the current state of the system and not on the path taken to reach that state.
Pressure $(P)$,volume $(V)$,and temperature $(T)$ are examples of state variables.
Work $(W)$ is a path function,meaning its value depends on the specific process or path followed to transition between states.
Therefore,work does not characterise the thermodynamic state of matter.

(A) The zeroth law of thermodynamics states that if two systems are each in thermal equilibrium with a third system,then they are in thermal equilibrium with each other.
This law forms the basis for the measurement of temperature,as it allows us to define a property (temperature) that is the same for all systems in thermal equilibrium.
Therefore,the zeroth law provides the fundamental concept of temperature.
Since the reason correctly explains why the zeroth law leads to the concept of temperature,$(A)$ is true,$(R)$ is true,and $(R)$ is the correct explanation for $(A)$.