What is the final temperature of the system?

Question

In an insulated container, 0.800kg of water at 40.0degrees celcius is mixed with 0.500kg of ice at -15 degrees celcius . Find the final temperature of the system. The freezing point of water is 0degrees celcius.

Answer 1

Consider an equation describing the event

Q=Cp m(T2-T)
Q - heat required to change temperature
T is temperature at equilibrium
m - mass
Cp specific heat
and also
Qf = Cf m
Cf - specific heat of fusion (water-ice-ice- water)
let
m1= mass of water and
m2=mas of ice

Q(water 40C to T) -Q(ice at from -15C to 0)- Q(latent heat of melting at 0C) -Q(ice water warming up 0C to T) =0

Cp1 m1(40c - T) - Cp2 m2(0 - (-15c) ) - Cf m2 - Cp1m2(T-0)=0
now just solve for T
Cp1 (water liquid) = 4.1813 J /(g K)
Cp2 (water solid) = 2.114 J/(g K)
Cf (ice)= 334 J/g

In this case since we looking at the differences deg K and deg C are interchangeable

Now just solve for T