Question

The fraction of ice that melts by mixing equal masses of ice at $-{10}^{o}C$ and water at ${60}^{o}C$ is :

• A. $\frac{6}{11}$
• B. $\frac{11}{16}$
• C. $\frac{5}{16}$
• D. $\frac{11}{15}$

Answer 1

Answer: (C)

$\frac{5}{16}$

Let in be initial masses and water and ice and $x$ be the mass of ice melting . So, Heat absorbed $=ms|\Delta T_{ice}|+x{L}_f$

$\Delta \theta$ absorbed $=m\left(1\right)\left(10\right)+x\left(80\right)$

Heat released $=ms\Delta Twater$

$\Delta H$ released $=m\left(1\right)\left(60\right)$

$\Delta H$ released $=60m$

As $\Delta \theta$ observed $=\Delta H$ released

$\Rightarrow 10m+80x=60m$

$\Rightarrow 80x=50m\Rightarrow x=\frac{5}{8}m$

Fraction of ice melted $=\frac{x}{2m}=\frac{5}{8}m=\frac{5}{16}$

Option C is correct