Understanding the distinction between extensive and intensive properties is a fundamental concept in chemistry and physics. Unlike intensive properties—such as temperature, density, or color—extensive properties scale directly with the size of the sample. On top of that, common examples include mass, volume, length, and total energy. When faced with a multiple-choice question asking which of the following is an extensive property of matter, the correct answer will always be a characteristic that depends on the amount of substance present. This article provides a complete walkthrough to identifying extensive properties, explaining the underlying science, and offering strategies to solve related problems confidently.
Defining Extensive Properties of Matter
An extensive property is a physical quantity whose value is proportional to the size of the system it describes. If you cut the sample in half, the property value is halved. Now, in simpler terms, if you double the amount of matter in a sample, the value of an extensive property doubles. This additive nature is the defining hallmark of these properties.
Consider a block of gold. That's why if you have a 10-gram sample and combine it with another 10-gram sample, the resulting 20-gram sample has twice the mass, twice the volume, and twice the heat capacity. In real terms, these are all extensive properties. They are extensive because they extend across the physical quantity of the material.
The Mathematical Perspective
From a thermodynamic standpoint, extensive properties are homogeneous functions of the first degree with respect to the number of particles (or moles) in the system. Mathematically, if a property $Y$ is extensive, then for a scaling factor $\lambda$:
$Y(\lambda n_1, \lambda n_2, ...) = \lambda Y(n_1, n_2, ...)$
Where $n$ represents the amount of substance. This formal definition underscores why mass ($m$), volume ($V$), internal energy ($U$), enthalpy ($H$), entropy ($S$), and Gibbs free energy ($G$) are classified as extensive.
Extensive vs. Intensive Properties: The Critical Comparison
To correctly answer "which of the following is an extensive property," you must be able to distinguish them from intensive properties. In real terms, intensive properties are independent of the amount of matter. They are intrinsic to the material's identity and do not change if the sample size changes.
| Feature | Extensive Properties | Intensive Properties |
|---|---|---|
| Dependence on Amount | Yes (Directly proportional) | No (Independent) |
| Additivity | Additive (Sum of parts = Whole) | Non-additive (Average of parts) |
| Identity Role | Does not identify substance | Identifies substance |
| Examples | Mass, Volume, Length, Total Charge, Heat Capacity, Entropy, Enthalpy | Temperature, Density, Pressure, Color, Boiling Point, Melting Point, Specific Heat, Refractive Index |
The "Cut the System in Half" Test
The most reliable mental shortcut for exam questions is the Division Test. Imagine cutting the system into two equal halves.
- Mass: Each half has half the mass. Extensive.
- Volume: Each half has half the volume. Extensive.
- Temperature: Each half has the same temperature. Intensive.
- Density: Each half has the same density. Intensive.
- Boiling Point: Each half boils at the same temperature. Intensive.
If the value changes when the system size changes, it is extensive. If it stays the same, it is intensive.
Comprehensive List of Common Extensive Properties
When scanning answer choices, look for these standard extensive properties. Memorizing this list allows for rapid identification.
1. Mass ($m$)
The most fundamental extensive property. It measures the quantity of matter. Measured in kilograms (kg) or grams (g).
2. Volume ($V$)
The three-dimensional space occupied by matter. Measured in liters (L), cubic meters ($m^3$), or milliliters (mL). Note: Molar volume ($V_m$) is intensive because it is volume per mole.
3. Length / Surface Area
Physical dimensions scale with size. A longer wire has more length and surface area Small thing, real impact. That's the whole idea..
4. Total Energy Forms
- Internal Energy ($U$): The total kinetic and potential energy of all particles in the system.
- Enthalpy ($H$): Total heat content ($H = U + pV$).
- Entropy ($S$): Measure of total disorder/number of microstates.
- Gibbs Free Energy ($G$): Energy available to do work.
- Helmholtz Free Energy ($A$): Energy available to do work at constant volume.
5. Heat Capacity ($C$)
The amount of heat required to raise the temperature of the entire object by one degree Celsius (or Kelvin). Units: J/K or J/°C Not complicated — just consistent..
- Crucial Distinction: Specific Heat Capacity ($c$) is intensive (J/g·K). Molar Heat Capacity ($C_m$) is intensive (J/mol·K). Only the total Heat Capacity ($C$) is extensive.
6. Electric Charge ($Q$)
Total charge scales with the number of charged particles.
7. Number of Moles ($n$)
A direct count of particles (Avogadro's number). Doubling the sample doubles the moles Not complicated — just consistent..
8. Momentum ($p$) and Kinetic Energy ($K$)
For a moving object, these depend on mass ($p=mv, K=1/2mv^2$), making them extensive.
Derived Intensive Properties: The Ratio Trick
A powerful concept in thermodynamics is that the ratio of two extensive properties is always an intensive property. This is how we derive specific values that identify substances regardless of sample size Simple, but easy to overlook. But it adds up..
$ \text{Intensive Property} = \frac{\text{Extensive Property}}{\text{Extensive Property}} $
| Ratio | Resulting Intensive Property |
|---|---|
| Mass / Volume | Density ($\rho$) |
| Volume / Moles | Molar Volume ($V_m$) |
| Internal Energy / Moles | Molar Internal Energy ($U_m$) |
| Enthalpy / Moles | Molar Enthalpy ($H_m$) |
| Entropy / Moles | Molar Entropy ($S_m$) |
| Heat Capacity / Mass | Specific Heat ($c$) |
| Heat Capacity / Moles | Molar Heat Capacity ($C_m$) |
| Charge / Volume | Charge Density |
If a question asks for an extensive property and offers "Density" or "Specific Heat" as options, you can immediately eliminate them because they are ratios of extensive properties.
Step-by-Step Strategy for Multiple Choice Questions
When you encounter the question "Which of the following is an extensive property of matter?" follow this workflow:
Step 1: List the Options
Write down the 4–5 choices provided (e.g., A) Temperature, B) Density, C) Mass, D) Boiling Point) Took long enough..
Step 2: Apply the "Size Dependence" Filter
Ask for each option: "If I take twice as much of this substance, does this value double?"
- Temperature: No. Boiling water is 100°C whether you have a cup or a bucket. → Intensive.
- Density: No. Gold is 19.3 g/cm³ whether it's a nugget or a bar. → Intensive.
- **Mass
…
- Mass: Yes. Consider this: **
- Boiling Point: No. The temperature at which a liquid boils does not change with the amount of liquid; a small pot and a large kettle both boil water at 100 °C (at the same pressure). And → **Extensive. If you take twice as much of the substance, the total mass doubles. → **Intensive.
No fluff here — just what actually works.
Having assessed each choice, move to the next step.
Step 3: Eliminate Intensive Candidates
Cross out any option that failed the “size‑dependence” test. In the example above, Temperature, Density, and Boiling Point are all intensive, leaving only Mass as a candidate.
Step 4: Verify with Units (Optional but Helpful)
Extensive properties typically carry units that scale with amount (e.g., kg, J, mol, C). Intensive properties are expressed per unit amount (e.g., J g⁻¹ K⁻¹, Pa, dimensionless). A quick unit check can confirm your elimination.
Step 5: Select the Answer
If exactly one option remains after Steps 2–4, that is the extensive property. If more than one survives (e.g., both Mass and Total Internal Energy appear), recall that any property that is directly proportional to the number of particles or the size of the sample qualifies; the question may allow multiple correct answers, so follow the test’s instructions (choose all that apply or pick the best fit).
Quick Practice
Question: Which of the following is an extensive property?
A) Specific heat capacity
B) Refractive index
C) Total enthalpy
D) pH
Solution:
- Specific heat capacity (J g⁻¹ K⁻¹) is intensive (per gram).
- Refractive index is dimensionless and independent of sample size → intensive.
- Total enthalpy (J) doubles when the sample doubles → extensive.
- pH is a logarithmic measure of hydrogen‑ion concentration; it does not scale with amount → intensive.
Answer: C) Total enthalpy.
Conclusion
Distinguishing extensive from intensive properties hinges on a simple mental experiment: does the value change proportionally when you take more or less of the substance? Here's the thing — by applying this size‑dependence test, optionally corroborating with units, and leveraging the fact that ratios of extensive quantities yield intensive ones, you can swiftly work through multiple‑choice questions. Mastering this strategy not only saves time during exams but also deepens your intuitive grasp of how thermodynamic scales with system size Worth keeping that in mind..
