If x gm of steam at `100^(@)`C is mixed with 5x gm of ice at `0^(@)C`, calculate the final temperature of resultiong mixture. The heat of vapourisation and fusion are 540 cal `gm^(-1)` and 80 cal `gm^(-1)` respectively.

Explanation

To solve the problem step by step, we will use the principles of thermodynamics, specifically the conservation of energy, which states that the heat lost by the steam will be equal to the heat gained by the ice.

### Step 1: Define the heat lost by steam
When steam at 100°C condenses into water at 100°C, it releases heat. The heat lost by the steam can be calculated as:

\[ \text{Heat lost by steam} = \text{mass of steam} \times \text{heat of vaporization} + \text{mass of water} \times \text{specific heat of water} \times (100 - T) \]
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