`1kg` ice at `-10^(@)C` is mixed with `1kg` water at `100^(@)C`. Then final equilirium temperature and mixture content.

Explanation

To solve the problem of mixing 1 kg of ice at -10°C with 1 kg of water at 100°C and finding the final equilibrium temperature and the mixture content, we can follow these steps:

### Step 1: Understand the Heat Transfer
When the ice and water are mixed, heat will be transferred from the water (which cools down) to the ice (which warms up and eventually melts). According to the principle of calorimetry, the heat lost by the water will be equal to the heat gained by the ice.

### Step 2: Define Variables
- Let \( m_{\text{ice}} = 1 \, \text{kg} \) (mass of ice)
- Let \( m_{\text{water}} = 1 \, \text{kg} \) (mass of water)
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