Constant Pressure Specific Heat (Cp) and Constant Volume Specific Heat (Cv) for Pure Substances

Introduction:
In thermodynamics, specific heat is a property that describes the amount of heat energy required to raise the temperature of a substance by a certain amount. It is usually expressed as specific heat capacity per unit mass or per mole of the substance. For pure substances, specific heat can be measured under constant pressure (Cp) or constant volume (Cv) conditions.

Difference between Cp and Cv:
The difference between Cp and Cv lies in the conditions under which they are measured.

Constant Pressure Specific Heat (Cp):
Cp is the specific heat capacity of a substance when the pressure remains constant during the heating process. It is defined as the amount of heat energy required to raise the temperature of a unit mass or unit mole of the substance by one degree Celsius under constant pressure conditions.

Constant Volume Specific Heat (Cv):
Cv is the specific heat capacity of a substance when the volume remains constant during the heating process. It is defined as the amount of heat energy required to raise the temperature of a unit mass or unit mole of the substance by one degree Celsius under constant volume conditions.

Approaching Zero as Absolute Temperature Approaches Zero:
The correct answer to the question is option 'B' - the difference between Cp and Cv approaches zero as the absolute temperature approaches zero. This can be explained by the behavior of gases at low temperatures.

At low temperatures, the kinetic energy of gas molecules decreases, and they move slower. As a result, the vibrational and rotational energies of the gas molecules become negligible compared to their translational kinetic energy. In other words, the internal energy of the gas is primarily associated with the motion of the gas molecules rather than their internal degrees of freedom.

Under these conditions, the specific heat at constant volume (Cv) approaches zero because there is very little contribution from the internal degrees of freedom. The gas molecules mainly gain or lose energy through their translational motion, which is related to the specific heat at constant pressure (Cp).

As the temperature approaches absolute zero, the gas molecules lose most of their kinetic energy and their motion becomes almost negligible. At this point, both Cp and Cv approach zero, and the specific heat capacity of the substance becomes negligible.

Conclusion:
In summary, the difference between constant pressure specific heat (Cp) and constant volume specific heat (Cv) for pure substances approaches zero as the absolute temperature approaches zero. This is because at low temperatures, the internal degrees of freedom of the gas molecules become negligible, and the specific heat capacity is primarily determined by the translational motion of the gas molecules.