Question

Four ice cubes at exactly 0 ∘C with a total mass of 51.5 g are combined with 160 g of water at 75 ∘C in an insulated container. (ΔH∘fus=6.02 kJ/mol, cwater=4.18J/g⋅∘C) . If no heat is lost to the surroundings, what is the final temperature of the mixture? Show Work

Answer 1

Let final temperature be T,

Heat gained by ice cube=m*[heat of fusion + C_water(T-0)]

                                                =51.5*(334 +4.18*T)

Heat lost by water=m_w*C_water*(75-T)

                                                =160*4.18*(75-T)

According to law of conservation of energy,

Heat gained by ice cube= Heat lost by water

51.5*(334 +4.18*T)=160*4.18(75-T)

T=37.28℃