First slide

Questions based on phase change

Question

2 kg of ice at $- 20^{0} C$ 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^-1 ⁰C^-1 and 0.5 kcal kg^-1 ⁰C^-1 while the latent heat of fusion of ice is 80 kcal kg^-1.

Moderate

A

7 kg
B

6 kg
C

4 kg
D

2 kg

Solution

Initially ice will absorb the heat to raise its temperature at 0⁰C, then its melting takes places.
If m_i = initial mass of ice, $m'_{i}$ = mass of ice that melts and
$m_{ω}$ = initial mass of water.
By law of mixture, heat gained by ice = heat lost by water
$\Rightarrow m_{1} \times c \times (20) + m_{i}^{'} \times L = m_{w} f_{w} (20)$
$\Rightarrow 2 \times 0.5 (20) + m'_{i}^{} \times 80 = 5 \times 1 \times 20 \Rightarrow m_{i}^{'} = 1 kg$
So, final mass of water = initial mass of water + mass of ice that melts
= 5 + 1 = 6kg

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App