In a steady state of heat conduction the temperature of the ends `A` and `B` of a rod `100cm` long per `0^(@)C` and `100^(@)C` The temperature of the rod at a point `60cm` distant from the end `A` is .

Options

A. `0^(@)C`
B. `40^(@)C`
C. `60^(@)C`
D. `100^(@)C`

Explanation

To solve the problem of finding the temperature at a point 60 cm from one end of a rod that is 100 cm long, with one end at 0°C and the other at 100°C, we can use the concept of steady-state heat conduction. Here’s a step-by-step solution:

### Step 1: Understand the setup
We have a rod of length 100 cm. The temperature at one end (point A) is 0°C and at the other end (point B) is 100°C. We need to find the temperature at a point 60 cm from point A.

### Step 2: Use the linear temperature gradient
In steady-state heat conduction, the temperature along the rod varies linearly between the two ends. This means we can use the formula for linear interpolation to find the temperature at any point along the rod.

### Step 3: Set up the formula
Let:
- \( T_A = 0°C \) (temperature at point A)
- \( T_B = 100°C \) (temperature at point B)
- \( L = 100 \, \text{cm} \) (total length of the rod)
- \( x = 60 \, \text{cm} \) (distance from point A)

The temperature \( T \) at a distance \( x \) from point A can be calculated using the formula:
\[ T = T_A + \left( \frac{T_B - T_A}{L} \right) \times x \]

### Step 4: Substitute the values
Substituting the known values into the formula:
\[ T = 0 + \left( \frac{100 - 0}{100} \right) \times 60 \]
\[ T = 0 + 1 \times 60 \]
\[ T = 60°C \]

### Step 5: Conclusion
The temperature at a point 60 cm from end A of the rod is **60°C**.

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