Question

2 kg of ice at – 20⁰C is mixed with 5 kg of water at 20⁰C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are 1 kcal/kg per ⁰C and 0.5 kcal/kg/⁰C while the latent heat of fusion of ice is 80 kcal/kg

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

Answer 1

Answer: (B)

6 kg

Answer 2

Initially ice will absorb heat to raise it's temperature to 0⁰C then it's melting takes place

If m = Initial mass of ice, m' = Mass of ice that melts and m_w = Initial mass of water

By Law of mixture Heat gain by ice = Heat loss by water

⇒ $m \times c \times (20) + m' \times L$ = $m_{w}c_{w}\lbrack 20\rbrack$

⇒ $2 \times 0.5(20) + m' \times 80$ = $5 \times 1 \times 20$ ⇒ $m'$ = 1kg

So final mass of water = Initial mass of water + Mass of ice that melts = 5 + 1= 6 kg.