Question

10 gm of ice at $-20{}^{o}C$ is added to 10 gm of water at $10{}^{o}C$. Then find the final temperature of the mixture.

Answer 1

If $\theta$ is resultant temperature.
$Heatlostbywater=Heatgainedbyice$
$(10\times 1\times (10-\theta \left)\right)=(10\times 0.5(20\left)\right)+(10\times 80)+(10\times 1(\theta -0\left)\right)$
But this gives $\theta =-40{}^{o}C$
This is not possible.
Ice cannot take heat from water at $0{}^{o}C$.
$Heatlostbywater=100cal.$
(when temperature falls to $0{}^{o}C$ )
$\Rightarrow$ Mixture attains $0{}^{o}C$ finally.