104 g of water at `30^@`C is taken in a calorimeter made of copper of mass 42 g. When a certain mass of ice at 0°C is added to it, the final steady temperature of the mixture after the ice has melted, was found to be `10^@`C. Find the mass of ice added. [Specific heat capacity of water = 4.2 J `g^(-1)""^@ C^(-1)`, Specific latent heat of fusion of ice = 336 J `g^(-1)`, Specific heat capacity of copper `= 0.4 Jg^(-1) ""^@ C^(-1)`].

Explanation

To solve the problem step by step, we will use the principle of conservation of energy, which states that the heat lost by the water and the calorimeter will be equal to the heat gained by the ice to melt and then warm up to the final temperature.

### Step 1: Calculate the heat lost by the water (Q1)
The formula for heat lost is:
\[ Q_1 = m_1 \cdot s_1 \cdot \Delta T_1 \]

Where:
- \( m_1 = 104 \, \text{g} \) (mass of water)
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