Question

$2$ kg of ice at $-20$${}^o$C is mixed with $5$ kg of H${}_2$O at ${20}^o$C in an insulating vessel having negligible heat capacity. Calculate the final mass of water left in the container.
Given: Specific heats of water and ice are $1$ kcal kg${}^{-1}$ ${}^o$C${}^{-1}$ and $0.5$ kcal kg${}^{-1o}$C${}^{-1}$ and latent heat of fusion of ice is $80$ k cal kg${}^{-1}$.

• A. 7 kg
• B. 6 kg
• C. 4 kg
• D. 2 kg

Answer 1

Answer: (B)

6 kg

Applying heat lost=heat gained
$m_{ice}^{\prime }L+m_{ice}20\left(0.5\right)=m_W\left(1\right)\left(20\right)$
$m_{ice}^{\prime }80=5\times 20-2\times \left(20\right)\times 0.5=80$
$\therefore m_{ice}^{\prime }=1kg$
Hence total amount of water $=6kg$.