Identify the material having high coefficient of volume expansion.
Understanding Coefficient of Volume Expansion in Materials
When materials are heated, they tend to expand in size. This phenomenon is known as thermal expansion. The extent to which a material expands upon heating is quantified by its coefficient of thermal expansion. For volume expansion, we use the coefficient of volume expansion, often denoted by the symbol \(\beta\) (beta).
The coefficient of volume expansion is defined as the fractional change in volume per degree Celsius (or Kelvin) change in temperature. A material with a high coefficient of volume expansion will experience a larger change in volume for a given change in temperature compared to a material with a low coefficient.
Comparing Volume Expansion Coefficients
Let's examine the approximate coefficient of volume expansion for the materials listed in the options: Brass, Alcohol, Glass, and Water. It's important to note that these values can vary slightly depending on the specific composition (for alloys like brass or glass) and the temperature range (especially for water).
| Material | Approximate Coefficient of Volume Expansion (\(\beta\)) in (\(10^{-6} \text{/}^\circ\text{C}\)) |
|---|---|
| Brass | 57 |
| Alcohol (Ethanol) | 1120 |
| Glass (Soda-lime) | 27 |
| Water (around room temp) | 210 |
By comparing the values in the table, we can clearly see which material has the highest coefficient of volume expansion:
- Glass has a relatively low coefficient (\(\approx 27 \times 10^{-6} \text{/}^\circ\text{C}\)), typical for solids.
- Brass, a metallic alloy, has a higher coefficient than glass but is still in the range for solids (\(\approx 57 \times 10^{-6} \text{/}^\circ\text{C}\)).
- Water has a significantly higher coefficient than solids, though its value varies with temperature (\(\approx 210 \times 10^{-6} \text{/}^\circ\text{C}\) around room temperature).
- Alcohol (Ethanol in this case) has a very high coefficient of volume expansion compared to the other options (\(\approx 1120 \times 10^{-6} \text{/}^\circ\text{C}\)).
Liquids generally have higher coefficients of volume expansion than solids because the intermolecular forces are weaker, allowing molecules to move further apart more easily when heated.
Conclusion: Material with High Volume Expansion
Based on the comparison of their approximate coefficients of volume expansion, Alcohol exhibits the highest value among the given options. Therefore, Alcohol is the material having a high coefficient of volume expansion.
Revision Table: Key Concepts in Thermal Expansion
| Concept | Description | Relevant Coefficient |
|---|---|---|
| Thermal Expansion | The tendency of matter to change in volume in response to changes in temperature. | Linear (\(\alpha\)), Area (\(\gamma\)), Volume (\(\beta\)) |
| Coefficient of Volume Expansion (\(\beta\)) | Fractional change in volume per unit change in temperature. Units are typically \(^\circ\text{C}^{-1}\) or \(\text{K}^{-1}\). | \(\beta = \frac{1}{V} \left(\frac{\partial V}{\partial T}\right)_P\) |
| Relationship between \(\alpha, \gamma, \beta\) (for isotropic solids) | For isotropic solids, \(\gamma \approx 2\alpha\) and \(\beta \approx 3\alpha\). |
Additional Information on Volume Expansion
The coefficient of volume expansion for liquids is generally much larger than for solids. This is why liquids in thermometers are visibly responsive to temperature changes. The expansion of gases is even greater, described by different gas laws (like the ideal gas law), but thermal expansion also applies. For anisotropic solids (materials where properties vary with direction), the expansion might be different along different axes, requiring multiple coefficients of linear expansion.
It's also worth noting the anomalous expansion of water between \(0^\circ\text{C}\) and \(4^\circ\text{C}\), where its volume decreases upon heating (or expands upon cooling), meaning its coefficient of volume expansion is negative in this specific temperature range. However, above \(4^\circ\text{C}\), water expands normally upon heating, and its coefficient is positive, as shown in the table for room temperature.
Similar Questions
Greater the value of _______ of a material, the more rapidly it will conduct heat.
Identify the material having low coefficient of volume expansion
Identify the material having the lowest coefficient of linear expansion.
- The thermal coefficient of linear expansion of a material is \(\alpha\). Then the thermal coefficient of its volume expansion will be
- When 1 kg of water is cooled from \(4^{\circ}C\) to \(0^{\circ}C\), its volume _____.
Important Questions from Thermal expansion
Thermal expansion of solids are:
A copper rod and a steel rod are to have lengths LC and LS, such that the difference between their lengths is the same at all ambient temperatures. If the coefficients of linear expansion of copper and steels are αC and αS respectively. The lengths are related to the coefficient of linear expansion as :
How much should the temperature of a brass rod be increased so as to increase its length by 1%?
Given: for brass α = 0.00002/°CA wooden wagon wheel has an outside diameter of 3750 mm. The iron tire for this wheel is deliberately made smaller so that it can be shrunk in place to be a tight fit. If the tire's inside diameter is 3737 mm at 20°C, the temperature to which it must be heated to fit over the wheel? The coefficient of linear expansion of the steel is 1.2 × 10-5/°C.
A cylinder of cross-sectional radius 1 cm and height 4 cm is heated from 0°C to 100°C. If the coefficient of linear expansion α = 4 × 10-4/°C, what will be the increase in the volume of the cylinder?
