Question

$5 \,kg$ of ice at $0^{\circ}C$ is mixed with $20 \,kg$ of water at $15^{\circ}C$. The final temperature of mixture is (Given : specific heat of water $= 1 \,cal\, g^{-1}\,{}^{\circ}C^{-1}$, latent heat of fusion of ice $= 80 \,cal \,g^{-1}$)

• A. $-4^{\circ}C$
• B. $0^{\circ}C$
• C. $4^{\circ}C$
• D. $3^{\circ}C$

Answer 1

Answer: (A)

Let $T$ is temperature of mixture.
Heat lost by water $=$ Heat gained by ice to melt $+$ Heat gained by water formed from ice
$20 \times 1 (15 - T) = 5 \times 80 + 5 \times 1 ( T - 0)$
$300 - 20T = 400 + 5T$
$-25 T = 100$
$T = -4^{\circ}C$