Question

What is the amount of heat energy required to convert ice of mass 20 Kg at $-4^{0}C$ to water at ${20}^{0}C$? Use the relevant option for calculation.
a) Latent heat of fusion of ice 3.34 x ${10}^5$ J / Kg.
b) Specific heat capacity of water is 4180 J / Kg / K
c) Specific heat of ice 2093 J / Kg / K

Answer 1

Given: ice of mass 20 Kg at $-4^{0}C$ to water at ${20}^{0}C$

To find: the amount of heat energy required to convert ice to water

Solution:

As per the given condition,

Latent heat of fusion of ice, $L=3.34\times {10}^{5}J/Kg.$

Specific heat capacity of water, $s=4180J/Kg/K$

Specific heat of ice, $c=2093J/Kg/K$

Mass of ice, $m=20kg$

The total heat required will be sum of heat energy needed to change the temperature of ice from $–4°C$ to $0°C$ plus heat required to undergo a solid to liquid phase change at its melting point plus heat required to heat the sample from $0^{\circ }C$ to ${20}^{\circ }C$

$q_{total}=q_1+q_2+q_3⟹q_{total}=mc\left(\Delta T\right)+mL+ms\left(\Delta T\right)⟹q_{total}=20\times 2093\times (0-(-4\left)\right)+20\times 3.34\times {10}^5+20\times 4180(20-0)⟹q_{total}=167440+66.8\times {10}^5+1672000⟹q_{total}=8519440J=8.52\times {10}^{3}kJ$

is the quantity of heat is required to transform the ice into water