The rate of flow of heat through a metal bar of area of cross-section 1 `m^2` when temperature gradient is `1^@C//m` under steady state is called

Options

A. thermal resistance
B. thermal conductivity
C. diffusibility
D. resistivity

Answer

To solve the question, we need to understand the concept of heat transfer and the relevant definitions. The question asks about the rate of flow of heat through a metal bar under a specific temperature gradient.

### Step-by-Step Solution:

1. **Understand the Concept of Heat Current:**
- Heat current (or heat transfer rate) is defined as the rate at which heat energy is transferred through a material. It is analogous to electric current in that it measures the flow of energy.

2. **Identify the Given Parameters:**
- Area of cross-section (A) = 1 m²
- Temperature gradient (dT/dx) = 1 °C/m
- Steady state implies that the heat flow is constant over time.

3. **Use the Formula for Heat Current:**
- The formula for heat current (H) through a material is given by:
\[ H = k \cdot A \cdot \frac{dT}{dx} \]
- Where:
- \( H \) = Heat current (W)
- \( k \) = Thermal conductivity (W/m·K)
- \( A \) = Area of cross-section (m²)
- \( \frac{dT}{dx} \) = Temperature gradient (°C/m or K/m)

4. **Substituting the Given Values:**
- Since \( A = 1 \, \text{m}^2 \) and \( \frac{dT}{dx} = 1 \, \text{°C/m} \):
\[ H = k \cdot 1 \cdot 1 = k \]
- This shows that the heat current is equal to the thermal conductivity when the area is 1 m² and the temperature gradient is 1 °C/m.

5. **Conclusion:**
- The question specifically asks for the term that describes the rate of flow of heat under the given conditions. The answer is **thermal conductivity**.

### Final Answer:
The rate of flow of heat through a metal bar of area of cross-section 1 m² when the temperature gradient is 1 °C/m under steady state is called **thermal conductivity**.

---