The thermal conductivity of a rod depends on

Options

A. length
B. mass
C. area of x-section
D. material of the rod

Explanation

To determine the factors on which the thermal conductivity of a rod depends, we can analyze the concept of thermal conductivity and its relationship with the properties of materials.

### Step-by-Step Solution:

1. **Understanding Thermal Conductivity**:
Thermal conductivity (K) is a material property that indicates how well a material can conduct heat. It is defined as the amount of heat (dq) that passes through a unit area (A) of the material in a unit time (dt) when there is a temperature gradient (ΔT) across a distance (dx).

2. **Formula for Heat Transfer**:
The heat transfer through conduction can be expressed using Fourier's law:
\[ \frac{dq}{dt} = -K \cdot A \cdot \frac{\Delta T}{dx} \]
Here, K is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and dx is the length of the rod.

3. **Factors Affecting Thermal Conductivity**:
- **Material of the Rod**: The thermal conductivity is primarily dependent on the type of material. Different materials have different intrinsic properties that affect how easily heat can flow through them. For example, metals like copper have high thermal conductivity due to the presence of free electrons.
- **Cross-sectional Area (A)**: While the thermal conductivity itself is a property of the material, the rate of heat transfer does depend on the area through which heat is conducted. A larger area allows more heat to flow.
- **Length of the Rod (dx)**: The length of the rod does not affect the thermal conductivity itself but affects the temperature gradient. A longer rod will have a greater temperature drop for the same amount of heat transferred.
- **Mass**: The mass of the rod does not directly affect thermal conductivity; however, it can influence the heat capacity of the rod, which is a different property.

4. **Conclusion**:
The thermal conductivity of a rod primarily depends on the material of the rod. Other factors like length and cross-sectional area influence the heat transfer rate but do not change the thermal conductivity value for a given material.

### Final Answer:
The thermal conductivity of a rod depends on the material of the rod.