What will be the final temperature when 150 g of ice at `0^@C` is mixed with 300 g of water at `50^@C`. Specific heat of water `=1 cal//g//^@C`. Latent heat of fusion of ice `=80 cal//g`.

Explanation

To solve the problem of finding the final temperature when 150 g of ice at 0°C is mixed with 300 g of water at 50°C, we can follow these steps:

### Step 1: Understand the Heat Exchange
When ice is mixed with warm water, the warm water will lose heat while the ice will gain heat. The heat lost by the water will be equal to the heat gained by the ice and the water formed from the melted ice.

### Step 2: Set Up the Heat Loss and Gain Equations
Let \( T \) be the final temperature of the mixture. The heat lost by the water can be expressed as:
\[ Q_{\text{lost}} = m_{\text{water}} \cdot c_{\text{water}} \cdot (T_{\text{initial, water}} - T) \]
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