A square is made of four rods of same material one of the diagonal of a square is at temperature difference `100^@C`, then the temperature difference of second diagonal:

Options

A. `0^(@)C`
B. `100/l`
C. `100/(2l)`
D. `100^(@)C`

Explanation

To solve the problem, we will analyze the heat transfer through the square made of four rods of the same material. We will denote the corners of the square as A, B, C, and D.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We have a square with corners A, B, C, and D.
- The temperature difference along one diagonal (let's say BD) is given as \( T_D - T_B = 100^\circ C \).

2. **Understand the Heat Flow:**
- Since all rods are made of the same material, they have the same thermal resistance (R).
- The heat current (I) flowing through each rod can be expressed as:
\[ I = \frac{\Delta T}{R} \]
- Here, \(\Delta T\) is the temperature difference across the rod.

3. **Set Up the Equations:**
- For the diagonal BD:
\[ I_{BD} = \frac{T_D - T_B}{R} \]
- For the diagonal AC:
\[ I_{AC} = \frac{T_A - T_C}{R} \]

4. **Equate the Heat Currents:**
- Since the rods are identical, the heat current through each rod must be equal:
\[ I_{BD} = I_{AC} \]
- This leads to:
\[ \frac{T_D - T_B}{R} = \frac{T_A - T_C}{R} \]
- We can cancel R from both sides:
\[ T_D - T_B = T_A - T_C \]

5. **Substitute the Known Temperature Difference:**
- We know \( T_D - T_B = 100^\circ C \), so we can substitute this into the equation:
\[ 100^\circ C = T_A - T_C \]

6. **Conclusion:**
- Rearranging gives us:
\[ T_A - T_C = 100^\circ C \]
- Therefore, the temperature difference along the second diagonal (AC) is also \( 100^\circ C \).

### Final Answer:
The temperature difference of the second diagonal (AC) is \( 100^\circ C \).

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