A container of negligible heat capacity contains `1kg` of water. It is connected by a steel rod of length `10m` and area of cross-section `10cm^(2)` to a large steam chamber which is maintained at `100^(@)C`. If initial temperature of water is `0^(@)C`, find the time after which it beomes `50^(@)C`. (Neglect heat capacity of steel rod and assume no loss of heat to surroundings) (use table `3.1`, take specific heat of water `=4180 J//kg.^(@)C)`

Explanation

To solve the problem of finding the time taken for 1 kg of water to heat from 0°C to 50°C through a steel rod connected to a steam chamber at 100°C, we can follow these steps:

### Step 1: Understand the Heat Transfer Mechanism
The heat transfer occurs through conduction via the steel rod. The heat gained by the water will equal the heat lost by the steam chamber.

### Step 2: Write the Heat Gain Equation for Water
The heat gained by the water can be expressed using the formula:
\[ Q = m \cdot s \cdot \Delta T \]
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