How much ice (at 0°c) must be added to 1.75 kg of water at 77 °c so as to end up with all liquid at 26 °c? (ci = 2000 j/(kg.°c), cw = 4186 j/(kg.°c), lf= 3.35 × 10 5 3.35×105 j/kg, lv= 2.26 × 10 6 2.26×106 j/kg)

To solve this problem it is necessary to apply the conservation equations of Energy.

By definition we know that the energy that is lost by water is totally equivalent to the energy gained by ice.

The energy lost by water could be defined as

Where,

mass of water

Specific Heat of Water

Change in Temperature

On the other hand the energy gained by ice can be defined as

Where,

Mass of ice

Latent heat of fusion

Specific heat of Ice

Change in Temperature

As the two energies are in balance then

Re-arrange to find

Therefore there must be 0.9653Kg of Ice