A vessel of negligible heat capacity contains 5-0 kg of water at `50^@`C. If 5.0 kg of ice at `0^@`C is added to it, find : (i) heat energy imparted by water in fall of its temperature from `50^@`C to `0^@`C, (ii) mass of ice melted, (iii) final temperature of mixture, and (iv) mass of water at `0^@`C in mixture. Given : specific heat capacity of water = 4200 J `kg^(-1) K^(-1)`, specific latent heat of ice = 336 kJ `kg^(-1)`.

Explanation

To solve the problem step by step, let's break it down according to the parts of the question.

### Given Data:
- Mass of water, \( m_w = 5.0 \, \text{kg} \)
- Initial temperature of water, \( T_{w_i} = 50^\circ C \)
- Mass of ice, \( m_i = 5.0 \, \text{kg} \)
- Initial temperature of ice, \( T_{i_i} = 0^\circ C \)
- Specific heat capacity of water, \( c_w = 4200 \, \text{J kg}^{-1} \text{K}^{-1} \)
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