Question

Identify the pair in which both are not extensive properties.

• A. Internal energy, enthalpy
• B. Mass, volume
• C. Density, pressure
• D. Heat capacity, Gibbs energy

Hint:

Property Classification:

• Extensive: Mass, volume, enthalpy, internal energy, Gibbs energy, entropy.
• Intensive: Pressure, temperature, density, refractive index, specific heat.
• Ratios of extensive properties (e.g., density = mass/volume) are often intensive.

Answer 1

The Correct Option is C

• Extensive properties depend on the quantity of matter. Doubling the system doubles the value.
• Intensive properties are independent of the quantity of matter. Their value remains constant even if the system is divided.

Review of each option:

• (1) Internal energy and enthalpy: Both are extensive.
• (2) Mass and volume: Both are extensive.
• (3) Density and pressure: Both are intensive.
• (4) Heat capacity and Gibbs energy: Both are extensive.

So, the only correct pair where both are not extensive is option (3): Density and Pressure.

Answer 2

Step 1: Define extensive and intensive properties
Properties of matter are classified into two categories: extensive and intensive.
- Extensive properties depend directly on the amount or size of the substance present. Examples include mass, volume, total energy, and enthalpy. If the quantity of the substance changes, these properties change proportionally.
- Intensive properties do not depend on the quantity of the substance. They remain the same regardless of the size of the sample. Examples include density, pressure, temperature, boiling point, and color.

Step 2: Analyze density
Density is defined as the mass per unit volume of a substance:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Even if the amount of substance changes (say, by taking half or double the sample), the ratio of mass to volume remains constant for a pure substance at a given temperature and pressure. Therefore, density does not depend on the amount of material and is an intensive property.

Step 3: Analyze pressure
Pressure is the force exerted per unit area:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \]
In fluids, pressure at a point depends on depth, temperature, and the nature of the fluid but not on the volume of the fluid or the size of the container. This makes pressure an intensive property. For example, if you take half of a gas in a container, the pressure does not necessarily change if temperature and volume conditions are kept constant.

Step 4: Compare with extensive properties
Extensive properties, unlike density and pressure, increase or decrease proportionally with the size or amount of the system. For example, mass doubles if the sample size doubles.

Step 5: Conclusion
Since density and pressure are independent of the amount of substance, both are intensive properties, meaning they are not extensive properties.
Therefore, the correct answer is that the pair density and pressure are both not extensive properties.