Question

$1\text{kg}$ of ice at $-{10}^{\circ }\text{C}$ is mixed with $4.4\text{kg}$ of water at ${30}^{\circ }\text{C}$. The final temperature of mixture is

Given specific heat of ice $=0.5{\text{cal/g}}^{\circ }\text{C}$,
Specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$,
Latent heat of fusion for ice $=80\text{cal/g}$.

• A. ${2.3}^{\circ }\text{C}$
• B. ${4.4}^{\circ }\text{C}$
• C. ${5.3}^{\circ }\text{C}$
• D. ${8.7}^{\circ }\text{C}$

Answer 1

The correct option is D ${8.7}^{\circ }\text{C}$

$1\text{kg}$ ice at $-{10}^{\circ }\text{C}+4.4\text{kg}$ of water at ${30}^{\circ }\text{C}$
Let $T$ be final temperature of mixture,
Heat gain by ice= Heat lost by water
$1000\times \frac{1}{2}\times 10+1000\times 80+1000(T-0)=4.4\times 1000\times 1\times (30-T)$
$5.4T=4.4\times 30-85$
$\Rightarrow T={8.7}^{\circ }C$