Question

50 g of ice 0${}^{\circ }C$ is added to 300 g of a liquid at 30${}^{\circ }C$. What will be the final temperature of the mixture when all the ice has melted? The specific heat capacity of the liquid is 2.65 $J{g}^{-1}{}^{\circ }{C}^{-1}$ while that of water is 4.2 $J{g}^{-1}{}^{\circ }{C}^{-1}$ . Specific latent heat of fusion of ice = 336 J $g^{-1}$.

• A. 7⁰C
• B. 5⁰C
• C. 13⁰C
• D. 20⁰C

Answer 1

The correct option is A

7⁰C

Let the final temperature of the mixture be t

According to the principle of mixtures,

Heat lost by liquid = Heat gained by ice

$300g\times 2.65J{g}^{-1}{}^{\circ }{C}^{-1}\times (30-t{)}^{\circ }C=50g\times 336J{g}^{-1}+50g\times 4.2J{g}^{-1}{}^{\circ }{C}^{-1}\times (t-0{)}^{\circ }C$
$t=7^{\circ }C$