Study Notes: Intensive and Extensive Properties, Moles, Entropy, Energy, Momentum

Page 1: Intensive Property

Definition: An intensive property is a property that stays the same regardless of how much material you have. It does not depend on the quantity.
Examples and explanations:
- Melting point of ice: 0^\circ\text{C}; ice will always melt at 0°C, whether you have a tiny piece or a whole block.
- Boiling point of water: 100^\circ\text{C}; remains the same regardless of quantity.
- Density of water: \rho = \frac{m}{V}; for water, density is about \rho \approx 1\ \text{g/cm}^3; remains the same whether you have a drop or a cup.
- Viscosity: water has low viscosity; honey has high viscosity (thickness).
- “Thick” vs “Runny”: high viscosity = thick, low viscosity = runny; this is an intensive property (not dependent on amount).
- Scale examples: a cup of water vs the ocean; a drop vs a pool; the property (viscosity, density, boiling/melting point) remains the same across scales.
Key takeaway: Intensive properties tell you about the material itself, not about how much of it you have.

Hardness of copper:
- Copper’s hardness is an intensive property; it remains the same whether you have a small piece or a big piece.
Elasticity:
- Both tiny and large rubber bands are elastic; they stretch and return, and this ability does not depend on the size of the band.
Color:
- Copper color is independent of piece size; it remains essentially the same (not strictly defined as ‘reddish’ for all copper forms in all contexts, but size does not change the color).
Practical note: These examples illustrate how intensive properties are invariant to amount or size.

Definition: An extensive property depends on the amount of material present; it changes when you add to or remove from the system.
Mass:
- Mass changes with how much material you have; if you break a stone into pieces, each piece has its own mass, and the total mass is the sum of the pieces. The mass of an individual piece is different from the mass of the whole, but the amount totally present is what scales.
Length:
- Length scales with the amount of material; e.g., two rods each 1 meter long give a total length of 2 meters.
Volume:
- Volume increases with more material; more material yields a bigger volume; less material yields a smaller volume.
Electrical charge (conceptual example):
- Rubbing a balloon on your hair produces a small charge; rubbing a balloon on a large carpet can produce a larger charge due to contact area and material interactions.
Summary: Extensive properties are proportional to the size or amount of the system.

Number of moles (extensive):
- Doubling the sample generally doubles the number of moles; halving the sample halves the number of moles.
- Relationship: n = \frac{m}{M} where n is the number of moles, m is mass, and M is the molar mass.
- Example for water: Water has molar mass M{\mathrm{H2O}} = 18.015\ \text{g/mol}.
- 18 g of water corresponds to 1 mole: n = \frac{18\ \,\text{g}}{18.015\ \text{g/mol}} \approx 1\ \text{mol}
- 36 g of water corresponds to 2 moles: n = \frac{36\ \text{g}}{18.015\ \text{g/mol}} \approx 2\ \text{mol}
Entropy (S):
- A measure of disorder or how spread out energy is in a system.
- Doubling the system generally increases the entropy (more possible microstates).
- Example: Ice cube melting → entropy increases because the solid (ordered) structure becomes more disordered liquid water.
Energy (E):
- More material typically means more total energy content (assuming similar conditions).
- Relationship: energy scales with amount of material, roughly proportional in many contexts.
- Everyday example: cookies and calories
- 1 cookie ≈ 100 calories
- 10 cookies ≈ 1,000 calories
Practical takeaway: Extensive properties track how much material you have, while intensive properties describe the material itself independent of amount.

Momentum concept:
- Momentum depends on mass and velocity.
- Formula: p = m \cdot v where p is momentum, m is mass, and v is velocity.
Examples:
- Ping-pong ball moving fast vs. a bowling ball moving at the same speed:
- The ping-pong ball has small momentum due to its small mass.
- The bowling ball has much larger momentum due to its larger mass, even if speeds are equal.
Units: momentum is measured in \text{kg} \cdot \text{m/s}.
Takeaway: For a given speed, heavier objects carry more momentum; for a given mass, faster objects carry more momentum.