Out of molar entropy (I), specific volume (II), heat capacity (III), volume (IV), extensive properties are : (a) I, II (b) I, II, IV (c) II, III (d) III, IV

Molar entropy, denoted by the symbol \( S \), is an extensive property that expresses the degree of disorder or randomness at the molecular level within a substance. Entropy is fundamental in determining the direction of spontaneous processes and the usability of energy in a system.

As an extensive property, molar entropy is proportional to the amount of substance. If you double the number of moles of gas in a container, assuming no change in temperature or pressure, the molar entropy would also double. This is because with more particles, there’s a greater number of possible microstates, or ways the particles can be arranged, which leads to higher entropy.
For example, the molar entropy of a gas increases when it expands into a vacuum—a process wherein the number of accessible microstates increases. Therefore, understanding molar entropy is crucial in predicting the spontaneity of chemical reactions and understanding the second law of thermodynamics.

Specific volume is an intensive property, meaning it is independent of the substance's quantity. It's the inverse of density and is defined as the volume occupied by a unit mass of a substance, typically represented by \( v \) and expressed in units such as cubic meters per kilogram \( (m^3/kg) \).

For homogeneous substances, specific volume is a convenient way to describe the substance as it doesn't change with size or extent of the sample. In the context of gases, specific volume is particularly helpful when analyzing thermodynamic processes, where temperature and pressure conditions can alter the volume of a mass of gas.
Despite being closely related to volume, which is an extensive property, specific volume is intensive because it describes a ratio that remains constant regardless of scale. For instance, whether you have one liter or a thousand liters of water, the specific volume remains the same, assuming pressure and temperature remain constant.

Heat capacity is the amount of heat required to raise the temperature of a substance by a certain temperature interval. It is often represented by \( C_p \) for constant pressure or \( C_v \) for constant volume conditions. Heat capacity can be an extensive property or an intensive property, depending on how it's expressed.

When heat capacity is given for a specific amount of substance—usually one mole—it becomes an intensive property known as molar heat capacity. When it is the total heat capacity for an entire system, it is an extensive property because it depends on the total amount of substance present.
For educational purposes, it's crucial to make the distinction clear: Specific heat capacity, also intensive, refers to the heat capacity per unit mass and remains constant for a substance, while total heat capacity, which is dependent on the material's mass or mole, will vary with the quantity.

Understanding the difference between intensive and extensive properties is a core concept in chemistry that is essential for solving many problems in thermodynamics and materials science. Intensive properties, such as temperature, pressure, and specific volume, do not depend on the amount of matter present. These properties are characteristic of the substance and can be used to identify it.

Extensive properties, like volume, mass, and molar entropy, on the other hand, change when the size of the sample changes. They are additive for multiple subsystems, which means that the total value of the property for the whole system is the sum of its values for the parts.
Knowing whether a property is intensive or extensive is important when analyzing system changes and calculating other properties. For instance, when combining two samples of water at different temperatures (an intensive property), the final temperature can be predicted through calculations that take into account the heat capacities (an extensive property when considered for the whole system) of both samples.