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 need to analyze the temperature distribution in the square formed by the four rods. Let's break it down step by step:

### Step 1: Understand the Setup
We have a square formed by four rods of the same material. One diagonal of the square has a temperature difference of \(100^\circ C\). We need to find the temperature difference across the second diagonal.

### Step 2: Define the Points
Let’s label the corners of the square as follows:
- Point A (bottom left corner)
- Point B (bottom right corner)
- Point C (top right corner)
- Point D (top left corner)

### Step 3: Assign Temperatures
Assume the temperature at point A is \(T\). Given that the temperature difference across one diagonal (A to C) is \(100^\circ C\), we can express the temperature at point C as:
- Temperature at C = \(T + 100^\circ C\)

### Step 4: Find the Temperature at Point B
Point B is the midpoint between points A and C. Therefore, we can calculate the temperature at point B as the average of the temperatures at A and C:
\[ T_B = \frac{T + (T + 100)}{2} = \frac{2T + 100}{2} = T + 50^\circ C \]

### Step 5: Find the Temperature at Point D
Similarly, point D is the midpoint between points A and B. Thus, the temperature at point D can be calculated as:
\[ T_D = \frac{T + (T + 50)}{2} = \frac{2T + 50}{2} = T + 25^\circ C \]

### Step 6: Calculate the Temperature Difference Across the Second Diagonal
Now, we need to find the temperature difference across the second diagonal (B to D):
- Temperature at B = \(T + 50^\circ C\)
- Temperature at D = \(T + 25^\circ C\)

The temperature difference across the second diagonal is:
\[ \Delta T = T_B - T_D = (T + 50) - (T + 25) = 50 - 25 = 25^\circ C \]

### Conclusion
Thus, the temperature difference across the second diagonal is \(25^\circ C\).