Question

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

• A. $0^{o}C$
• B. $1^{o}C$
• C. ${10}^{o}C$
• D. ${20}^{o}C$

Answer 1

The correct option is A $0^{o}C$

Heat lost by 5 g of water at ${30}^{o}C$ to water at $0^{o}C$.
$Q_L=5\times 1\times 30=150cal$
Heat required by 5 g of ice at $-{20}^{o}C$
$\left(Q_1\right)=5\times 0.5\times \left(2.0\right)=50cal$
Heat required by 5 g of ice at $0^{o}C$ into water at $0^{o}C$.
$\left(Q_2\right)=5\times 80=400cal$
$Q_L<(Q_1+Q_2)$
$\therefore$ The final temperature of the mixtuure is $0^{o}C$.