In a steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are `100^(@)C` and `0^(@)C` respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod

Options

A. `-30^(@)C`
B. `70^(@)C`
C. `5^(@)C`
D. None of the above

Answer

To find the temperature of the rod at a point that is 6 cm from end A, we can use the concept of linear temperature distribution in a steady state of thermal conduction.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Length of the rod (L) = 20 cm
- Temperature at end A (T_A) = 100°C
- Temperature at end B (T_B) = 0°C
- Distance from end A (d) = 6 cm

2. **Determine the Temperature Gradient:**
The temperature gradient (slope) can be calculated using the formula:
\[ \text{Temperature Gradient} = \frac{T_B - T_A}{L} = \frac{0°C - 100°C}{20 \text{ cm}} = \frac{-100°C}{20 \text{ cm}} = -5°C/\text{cm} \]

3. **Calculate the Temperature at 6 cm from End A:**
We can find the temperature at a distance of 6 cm from end A using the linear temperature distribution formula:
\[ T(x) = T_A + \left(\text{Temperature Gradient}\right) \times x \]
Where \( x \) is the distance from end A. Substituting the values:
\[ T(6 \text{ cm}) = 100°C + (-5°C/\text{cm}) \times 6 \text{ cm} \]
\[ T(6 \text{ cm}) = 100°C - 30°C = 70°C \]

4. **Final Answer:**
The temperature of the rod at a point 6 cm from end A is **70°C**.