In which of the following sets, all properties belong to same category (all extensive or all intensive) ?

Options

A. Mass, volume, pressure
B. Temperature, pressure, volume
C. Heat capacity, density, entropy
D. Enthalpy, internal energy, volume.

Answer

To determine which set of properties belongs to the same category (either all extensive or all intensive), we need to first understand the definitions of extensive and intensive properties:

1. **Extensive Properties**: These properties depend on the amount of substance present. Examples include mass, volume, and total energy.
2. **Intensive Properties**: These properties do not depend on the amount of substance present. Examples include temperature, pressure, and density.

Now, let's analyze each option provided in the question:

### Step 1: Analyze Option 1 - Mass, Volume, and Pressure
- **Mass**: Extensive property (depends on the amount of substance).
- **Volume**: Extensive property (depends on the amount of substance).
- **Pressure**: Intensive property (does not depend on the amount of substance).

**Conclusion**: This set contains both extensive and intensive properties. **Not all belong to the same category.**

### Step 2: Analyze Option 2 - Temperature, Pressure, and Volume
- **Temperature**: Intensive property (does not depend on the amount of substance).
- **Pressure**: Intensive property (does not depend on the amount of substance).
- **Volume**: Extensive property (depends on the amount of substance).

**Conclusion**: This set contains both extensive and intensive properties. **Not all belong to the same category.**

### Step 3: Analyze Option 3 - Heat Capacity, Density, and Entropy
- **Heat Capacity**: Extensive property (depends on the amount of substance).
- **Density**: Intensive property (does not depend on the amount of substance).
- **Entropy**: Extensive property (depends on the amount of substance).

**Conclusion**: This set contains both extensive and intensive properties. **Not all belong to the same category.**

### Step 4: Analyze Option 4 - Enthalpy, Internal Energy, and Volume
- **Enthalpy**: Extensive property (depends on the amount of substance).
- **Internal Energy**: Extensive property (depends on the amount of substance).
- **Volume**: Extensive property (depends on the amount of substance).

**Conclusion**: All properties in this set are extensive. **All belong to the same category.**

### Final Answer:
The correct option where all properties belong to the same category is **Option 4: Enthalpy, Internal Energy, and Volume**.

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