Question

PLEASE HELP ME WITH THIS ONE QUESTION
You have 1 kg of water and you want to use that to melt 0.1 kg of ice. What is the minimum temperature necessary in the water, to just barely melt all of the ice? (Lf = 3.33 x 105 J/kg, cwater 4186 J/kg°C)

Answer 1

Answer: $7.95^{\circ}C$

Explanation:

Given

Mass of water is $m_1=1\ kg$

mass of ice is $m_2=0.1\ kg$

Latent heat of fusion $L=3.33\times 10^5\ kJ/kg$

The heat capacity of water is $c_{w}=4186\ J/kg^{\circ}C$

Suppose water is at  $T^{\circ} C$  and it reaches to $0^{\circ}C$ to melt the ice

the heat released by water must be equivalent to heat absorbed by the ice

$\therefore \quad m_1c_w(T-0)=m_2\times L\\\Rightarrow 1\times 4186\times T=0.1\times 3.33\times 10^5\\\Rightarrow T=7.95^{\circ}C$