Question

Consider the following thermodynamic properties of a system: (i) Volume (ii) Pressure (iii) Density (iv) Heat capacity. The extensive property/properties of the system is/are

• A. (ii) and (iv)
• B. (iv) only
• C. (i), (ii) and (iii)
• D. (i) and (iv)
• E. (iii) and (iv)

Hint:

An easy way to remember: If you cut the system in half, an extensive property becomes half, while an intensive property remains the same.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Thermodynamic properties are classified into two types:
Extensive Properties: These properties depend on the mass or size of the system. Their value is directly proportional to the amount of substance present. Examples include mass, volume, internal energy, enthalpy, and heat capacity.
Intensive Properties: These properties are independent of the mass or size of the system. Their value does not change if the system is divided into smaller parts. Examples include temperature, pressure, density, and molar heat capacity.
Step 2: Detailed Explanation:
Let's analyze each property given:

(i) Volume: If you double the amount of a substance, its volume doubles (at constant temperature and pressure). Thus, volume is an extensive property.

(ii) Pressure: If you take a container of gas and divide it in half with a partition, the pressure in each half remains the same as the original pressure. Thus, pressure is an intensive property.

(iii) Density: Density is defined as mass per unit volume (\(\rho = m/V\)). If you double the mass of a substance, its volume also doubles, so the ratio (density) remains constant. Thus, density is an intensive property. It is a ratio of two extensive properties.

(iv) Heat capacity: Heat capacity is the amount of heat needed to raise the system's temperature by one degree. If you have twice the amount of substance, you will need twice the amount of heat to cause the same temperature change. Thus, heat capacity is an extensive property. (Note: Specific heat capacity and molar heat capacity are intensive).

The extensive properties from the list are Volume (i) and Heat capacity (iv).
Step 3: Final Answer:
The extensive properties are (i) and (iv). This corresponds to option (D).