Ice at $-20^{\circ} \mathrm{C}$ is added to $50 \mathrm{~g}$ of water at $40^{\circ} \mathrm{C}$, When the…

Ice at $-20^{\circ} \mathrm{C}$ is added to $50 \mathrm{~g}$ of water at $40^{\circ} \mathrm{C}$, When the temperature of the mixture reaches $0^{\circ} \mathrm{C},$ it is found that 20 $\mathrm{g}$ of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water $=4.2 \mathrm{~J} / \mathrm{g} /{ }^{\circ} \mathrm{C}$ Specific heat of Ice $=2.1 \mathrm{~J} / \mathrm{g} /{ }^{\circ} \mathrm{C}$ Heat of fusion of water at $\left.0^{\circ} \mathrm{C}=334 \mathrm{~J} / \mathrm{g}\right)$
  1. $50 \mathrm{~g}$
  2. $100 \mathrm{~g}$
  3. $60 \mathrm{~g}$
  4. $40 \mathrm{~g}$

Solution

Let m gram of ice is added. From principal of calorimeter heat gained (by ice) $=$ heat lost (by water) $\begin{array}{l} \therefore 20 \times 2.1 \times \mathrm{m}+(\mathrm{m}-20) \times 334 \\ =50 \times 4.2 \times 40 \\ 376 \mathrm{~m}=8400+6680 \\ \mathrm{~m}=40.1 \end{array}$

Asked in: JEE Main 2019 (11 Jan Shift 1)

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