Question

An insulated beaker with negligible mass contains liquid water with a mass of 0.235 kg and a temperature of 79.0 ∘C
How much ice at a temperature of -24.2 ∘C must be dropped into the water so that the final temperature of the system will be 30.0 ∘C ?

Take the specific heat of liquid water to be 4190 J/kg⋅K , the specific heat of ice to be 2100 KJ/kg⋅K , and the heat of fusion for water to be 3.34×10⁵ J/kg

M ice = ?

Answer 1

Suppose M kg of ice is needed to make the system.

As the final temperature of the system is the amount of heat the hot water will give away is,

Here is the mass, is the specific heat of water, and are final and initial temperature. So the water will loose the amount of heat,

Now to heat the ice from to , the ammount of heat nedded is,

is mass and specific heat of ice. So,

Now to melt the ice the heat needed is,

, is heat of fusion of ice

Now to heat the water from to , the ammount of heat nedded is,

So now,

So,

So the amount of ice needed is 0.0945 kg