Question

In a container of negligible mass, 0.200 kg of ice at an initial temperature of -36.0 ∘C is mixed with a mass m of water that has an initial temperature of 80.0∘C. No heat is lost to the surroundings.

If the final temperature of the system is 30.0 ∘C, what is the mass m of the water that was initially at 80.0∘C?

Answer 1

Heat gained by ice:

= heat gained by ice from (-36⁰C) to 0⁰C + heat gained by ice to convert into water at 0⁰C + heat gained by water at 0⁰C to 30⁰C

where c_i = 2.108 kJ/kgK (specific heat of ice) and c_w = 4.187 kJ/kgK (specific heat of water) and L = latent heat of fusion of ice = 334 kJ/kg

Now heat lost by water of mass m:

Now heat lost by water of mass m = Heat gained by ice

Then

Hence mass m of the water that was initially at 80.0∘C = 0.511 kg