Identify Intensive Properties Among Given Thermodynamic Variables

An intensive property is a physical or thermodynamic quantity whose value does not depend on the amount or size of the substance present in the system. Conversely, an extensive property depends on the mass, volume, or size of the system.

Let us evaluate each of the given options:

1. Molar conductivity ($\Lambda_m$):
   Molar conductivity is defined as the conductivity ($\kappa$) per unit molar concentration ($C$) of an electrolyte:
   $\Lambda_m = \frac{\kappa}{C}$
   Since both conductivity and concentration are intensive properties (or equivalently, molar conductivity is the ratio of an extensive property to the amount of substance), its value is independent of the total volume or total mass of the solution. Hence, molar conductivity is an intensive property.

2. Electromotive force ($E_{\text{cell}}$):
   The electromotive force (EMF) of a electrochemical cell is related to the standard Gibbs free energy change ($\Delta G$) by:
   $\Delta G = -n F E_{\text{cell}} \implies E_{\text{cell}} = -\frac{\Delta G}{n F}$
   Because $\Delta G$ (Gibbs free energy) and $n$ (moles of electrons transferred) are both extensive properties, their ratio $E_{\text{cell}}$ is independent of the size or scale of the cell. Thus, electromotive force is an intensive property.

3. Resistance ($R$):
   Electrical resistance of a conductor is given by:
   $R = \rho \frac{l}{A}$
   where $\rho$ is resistivity, $l$ is length, and $A$ is the cross-sectional area. Since resistance depends directly on the geometry and size of the system, doubling the length doubles the resistance. Therefore, resistance is an extensive property.

4. Heat capacity ($C$):
   Heat capacity is the amount of heat required to raise the temperature of a given body by $1\text{ K}$:
   $C = m \cdot c$
   where $m$ is the mass and $c$ is the specific heat capacity. Since $C$ depends directly on the mass of the substance, heat capacity is an extensive property (unlike molar heat capacity or specific heat capacity, which are intensive).

Therefore, the intensive properties are molar conductivity and electromotive force.

Correct Options: A and B