A metallic rod is continuously heated at its two ends, the flow of heat through the rod does not depend upon –

Options

A. The area of cross section of the rod
B. The mass of the rod
C. Time
D. The temperature gradient

Answer

To solve the question, "A metallic rod is continuously heated at its two ends, the flow of heat through the rod does not depend upon –", we will analyze the factors affecting heat flow in a metallic rod.

### Step-by-Step Solution:

1. **Understanding Heat Flow**:
The flow of heat through a material is described by Fourier's law of heat conduction, which states that the rate of heat transfer (dq/dt) through a material is directly proportional to the temperature difference (ΔT) across the material and the area (A) through which the heat is flowing, and inversely proportional to the length (L) of the material.

2. **Fourier's Law of Heat Conduction**:
The mathematical expression for Fourier's law is:
\[ \frac{dq}{dt} = -k \cdot A \cdot \frac{dT}{dx} \]
where:
- \( \frac{dq}{dt} \) = rate of heat flow
- \( k \) = thermal conductivity of the material
- \( A \) = cross-sectional area
- \( \frac{dT}{dx} \) = temperature gradient

3. **Identifying Factors Affecting Heat Flow**:
From the equation, we can see that:
- The rate of heat flow is **directly proportional** to the area (A) of the rod.
- The rate of heat flow is **directly proportional** to the temperature difference (ΔT) across the ends of the rod.
- The rate of heat flow is **inversely proportional** to the length (L) of the rod.

4. **Analyzing the Options**:
Now, let's analyze the options provided in the question:
- **Option 1**: Area of the rod – This affects heat flow (it is directly proportional).
- **Option 2**: Mass of the rod – This does not appear in the equation for heat flow, indicating that it does not affect the rate of heat transfer.
- **Option 3**: Time – The rate of heat flow is defined as heat transfer per unit time, thus it does depend on time.
- **Option 4**: Temperature difference – This affects heat flow (it is directly proportional).

5. **Conclusion**:
The only factor that does not affect the flow of heat through the rod is the **mass of the rod**. Therefore, the correct answer is **Option 2**.

### Final Answer:
The flow of heat through the rod does not depend upon the **mass of the rod**.

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