Resulting temperature of ice-water mixture – Rankers Physics
Topic: Thermal Physics
Subtopic: Calorimetry

Resulting temperature of ice-water mixture

When 150 gm of ice at \( 0^\circ\text{C} \) is mixed with 60 gm of water at \( 50^\circ\text{C} \) in a container, the resulting temperature is
\( 2.7^\circ\text{C} \)
\( 3.7^\circ\text{C} \)
\( 5.7^\circ\text{C} \)
\( 0^\circ\text{C} \)

Solution:

Heat lost by water to cool to \( 0^\circ\text{C} \) is \( Q_{\text{lost}} = m_w c_w \Delta T = 60 \times 1 \times 50 = 3000 \text{ cal} \). Heat needed to melt all ice is \( Q_{\text{melt}} = m_i L = 150 \times 80 = 12000 \text{ cal} \). Since \( Q_{\text{lost}} < Q_{\text{melt}} \), only a part of the ice melts, and the final temperature remains \( 0^\circ\text{C} \).

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