1 kcal of heat flowing through a rod of iron.When the rod is cut down to 4 pieces then what will be the heat flowing through each piece having same differential temperature ?

Options

A. 1/2 Kcal
B. 1/4 kcal
C. 1 Kcal
D. 1/15 Kcal

Explanation

To solve the problem step by step, we will analyze the situation of heat transfer through a rod of iron that is cut into four pieces.

### Step 1: Understand the Heat Transfer Equation
The rate of heat flow (Q) through a conductor can be described by the equation:
\[ Q = \frac{k \cdot A \cdot \Delta T}{L} \]
where:
- \( Q \) = heat transferred
- \( k \) = thermal conductivity of the material
- \( A \) = cross-sectional area of the rod
- \( \Delta T \) = temperature difference across the rod
- \( L \) = length of the rod

### Step 2: Initial Condition
Initially, we have a rod of iron that transfers 1 kcal of heat. This means:
\[ Q = 1 \text{ kcal} \]

### Step 3: Cutting the Rod
When the rod is cut into 4 equal pieces, the length of each piece becomes \( L/4 \) (where \( L \) is the original length of the rod).

### Step 4: Analyze the Heat Transfer in Each Piece
Since the pieces are identical in material and cross-sectional area, the thermal conductivity \( k \) and the area \( A \) remain the same for each piece. The temperature difference \( \Delta T \) across each piece is also the same as it was for the original rod.

### Step 5: Heat Flow Through Each Piece
Using the heat transfer equation, the heat flowing through each piece can be expressed as:
\[ Q_{\text{piece}} = \frac{k \cdot A \cdot \Delta T}{L/4} \]
This can be simplified to:
\[ Q_{\text{piece}} = 4 \cdot \frac{k \cdot A \cdot \Delta T}{L} \]
This means that the heat flow through each piece is four times the heat flow through the original length of the rod.

### Step 6: Conclusion
However, since the total heat transferred through the entire rod remains constant (1 kcal), and since the heat is distributed equally among the four pieces, the heat flowing through each piece is:
\[ Q_{\text{piece}} = \frac{1 \text{ kcal}}{4} = 0.25 \text{ kcal} \]

Thus, the heat flowing through each piece is **0.25 kcal**.

### Final Answer
The heat flowing through each piece is **0.25 kcal**.