Question

$19g$ of water at $30$ and $5g$ of ice at $\mathring{-20}C$ are mixed together in a calorimeter. What is the final temperature of the mixture? (Given specific heat of ice $=0.5cal{g}^{-1}{\left(\right)}^{-1}$ and latent heat of fusion of ice $=80cal{g}^{-1}$)

• A. $0$
• B. $-5$
• C. $5$
• D. $10$

Answer 1

The correct option is C $5$

Let the final temperature of mixture be $t$.
Heat lost by water in calories,
$H_1=19\times 1\times (30-t)$
$=570-19t$
Heat taken by ice, $H_2={ms}_i\Delta t+mL+{ms}_{w}t$
$=5\times \left(0.5\right)20+5\times 80+5\times 1\times t$
According to principle of calorimetry,
$H_1=H_2$
$5\times \left(0.5\right)\times 20+5\times 80+5t=570-19t$
$\Rightarrow 24t=570-450=120$
$\Rightarrow t=5$