A family enters a winter vacation cabin whose walls are adiabatic, initially the interior temperature is the same as the outside temperature `(0^(@)C)`. The cabin consists of a single room of floor area `6m` by `4m` and height `3m`. The room contains a `2kW` electric heater. Assuming that the room is perfectly airlight and that all the heat from the heater is absorbed by the air, none escaping through the walls. The time after the heater is turned on, the air temperature reaches the comfort level of `21^(@)C` in `x xx100 sec`, then find `x` (Take `C_(v)=20.8 J//mol-K`)

Explanation

To solve the problem, we need to calculate the time taken for the air temperature in the cabin to reach a comfortable level of \(21^\circ C\) from an initial temperature of \(0^\circ C\) using a \(2 kW\) electric heater. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the Volume of the Room
The volume \(V\) of the room can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given dimensions:
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