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Question

What will be the temperature, when 150 g of ice at 0°C is mixed with 300 g of water at 50°C? Specific heat of water =1 ca lg-1°C. Latent heat of fusion of ice = 80 -1 ca lg^{-1}.

Moderate

Solution

Let us assume that T > 0° C

Heat lost by water = Heat gained by ice to melt + heat gained by water formed from ice

$\begin{array}{l}300\times 1\times (50-\mathrm{T})=150\times 80+150\times 1\times (\mathrm{T}-0)\\ \Rightarrow \phantom{\rule{1em}{0ex}}\mathrm{T}=6{.7}^{\circ}\mathrm{C}\end{array}$

Hence, our assumption that T > 0°C is correct.

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