Question

Consider two 35-gram ice cubes, each initially at -5°C. One is dropped into a at container filled with 0.1 kg of liquid nitrogen (initially the boiling point of nitrogen); the other cube is dropped into a container filled with 1 kg of (liquid) water, initially at 5°C. Assume that no heat is lost through either container (or into the atmosphere).

1.Determine the final (equilibrium) temperature of the icewater mixture.

2. Determine the phase (ie., liquid or solid) corresponding to the equilibrium temperature you obtained in part 1.

Answer 1

a) initial temperature of water, tw = 5 C
final temperature = T
initial mass of water, m = 1 kg
initaial temperature of ice = -5C = ti
initial mass of ice . M = 0.035 kg
hence from heat conservation'
energy lost by ice energy gained by water
MLf * Mc(ti) + MC(T - ti) = mC(tw - T)
here, Lf is latent heat of fusion of water, c is heat capacity of ice, C is heat capacity of water
0.035(333550 + 2108*5 + 4187(T + 5)) = 1*4187(5 - T)
1. T = 1.8827 C
2. Final phase = liquid