For a class demonstration, your physics instructor pours 1.16 kg of steam at 100.0°C over 4.69 kg of ice at 0.0°C and allows the system to reach equilibrium. He is then going to measure the temperature of the system. While the system reaches equilibrium, you are given the latent heats of ice and steam and the specific heat of water: Lice = 3.33·105 J/kg, Lsteam = 2.26·106 J/kg, cwater = 4186 J/(kg °C). You are asked to calculate the final equilibrium temperature (in °C) of the system. What value do you find?

Answer 1

It is a simple technique: add the heats gained, and set that sum to zero.

HeatIcemelting+heatwater+heatsteamcondnesing + heatgained steam cooling=0

massice*Hc+ massice*cwater(Tf-0)+masssteam*Hv +masssteam*cw*(Tf-100)=0

solve for Tf.