Thermal Properties of Matter

JEE Main level, single correct, medium

78 of 126

Question 78 of 126

Ice at −20∘C-20^{\circ} \mathrm{C} is added to 50 g50 \mathrm{~g} of water at 40∘C40^{\circ} \mathrm{C}, When the temperature of the mixture reaches 0∘C,0^{\circ} \mathrm{C}, it is found that 20 g\mathrm{g} of ice is still unmelted. The amount of ice added to the

water was close to (Specific heat of water
=4.2 J/g/∘C=4.2 \mathrm{~J} / \mathrm{g} /{ }^{\circ} \mathrm{C}

Specific heat of Ice
=2.1 J/g/∘C=2.1 \mathrm{~J} / \mathrm{g} /{ }^{\circ} \mathrm{C}

Heat of fusion of water at
0∘C=334 J/g)\left.0^{\circ} \mathrm{C}=334 \mathrm{~J} / \mathrm{g}\right)

Show answer and solution

Answer: (D) 40 g40 \mathrm{~g}

Let m gram of ice is added. From principal of calorimeter heat gained (by ice) == heat lost (by water)

$\begin{array}{l}


\therefore 20 \times 2.1 \times \mathrm{m}+(\mathrm{m}-20) \times 334 \\


=50 \times 4.2 \times 40 \\


376 \mathrm{~m}=8400+6680 \\


\mathrm{~m}=40.1


\end{array}$

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