# A 10 kg block of ice has a temperature of -13 C. The pressure is one atmosphere. The block...

## Question:

A 10 kg block of ice has a temperature of -13 C. The pressure is one atmosphere. The block absorbs 4.10 106 J of heat.

What is the final temperature of the liquid water?

## Phase Change and Heat transfer:

The phase changes take place in the ice when the heat is provided to it. It converts from solid to the liquid as it reaches its melting point after providing heat to it.

Given Data

Mass of the block {eq}(m) = 10 \ kg {/eq}

Initial temperature of the block {eq}(T_{i1}) = -13^\circ {/eq}

Heat energy absorbed by it {eq}Q = 4.1 \times 10^{6} \ J {/eq}

Now, this heat will first raise the temperature to {eq}0^\circ C {/eq}, then the melting takes place

Therefore,

{eq}Q = mC_{ice}(0 - T_{i}) + mL + mC_{water}(T-0) \\ 4.1 \times 10^{6} = [ 10 \times (2.04 \times 10^{3})(0-(-13)) ] + (10 \times (335 \times 10^{3})) + [ 10 \times (4.18 \times 10^{3})(T-0)] \\ T = 111.598^\circ {/eq}

Where

• {eq}C_{ice} = 2.04 \ kJ/kg -k {/eq} is the specific heat of the ice
• {eq}L = 335 \ kJ/kg {/eq} is the latent heat of the ice
• {eq}C_{w} = 4.18 \ kJ/kg-k {/eq} is the specific heat of the water