a): Two 50 g ice cubes are dropped into 200 g of water in a thermally insulated container. If the water is initially at 25 degree Celsius, and the ice comes directly from a freezer at -15 degree Celsius, what is the final temperature at thermal equilibrium? b): What is the final temperature if only one ice cube is used?

Question

a):    Two 50 g ice cubes are dropped into 200 g of water in a thermally insulated container. If the water is initially at 25 degree Celsius, and the ice comes directly from a freezer at -15 degree Celsius, what is the final temperature at thermal equilibrium?   b): What is the final temperature if only one ice cube is used?

bobpursley · Answer

heat gained in anyting changing temp =mass*c*(tf-ti)
heat gained by melting ice: mass*Lf where Lf is the heat of fusion for ice per mass.

Now, when this happens in a closed system, everything has the same final temperature, and the sum of all heats gained is zero (some of them will be negative0.

Heat gained by ice/melted ice+heat gained by water=0

Ice:
massice*cice*(0-(-15)) + massice*Lf + massmelted ice*cwater*(Tf-0)
Waterinitial
masswater*cwater*(Tf-25)

set both of these equal, and solve for Tf.