Question

You drop an ice cube into an insulated flask full of water and wait for the ice cube to completely melt. The ice cube initially has a mass of 60.0 g and a temperature of 0°C. The water (before the ice cube is added) has a mass of 760 g and an initial temperature of 20.0°C. What is the final temperature (in °C) of the mixture? (Assume no energy is lost to the walls of the flask, or to the environment.)

Answer 1

Answer:$T=12.69^{\circ}C$

Explanation:

Given

Mass of ice $m=60 gm$

mass of water $M=760 gm$

Initial Temperature of water $T_i=20^{\circ}C$

Let T be the Final Temperature of mixture

Latent heat of Fusion $L=334 J/gm$

heat required to melt ice completely is

$Q_1=60\times 334=20.04 kJ$

Heat released by water is taken by ice thus

$Mc_{water}(20-T)=mL+mc_{water}(T-0)$

$0.76\times 4.184\cdot (20-T)=20.04+0.06\times 4.184\cdot (T)$

$T=12.69^{\circ}C$