Question

An ice cube whose mass is 50 g is taken from a freezer at a temperature of -10C and then dropped into a cup of water at 0C. If no heat is gained or lost from the outside, how much water will freeze onto the cup?

Answer 1

Given:

1. Mass of ice cube, mc = 50 g

2. Temperature of ice cube, tc= -10C

3. temperature of water in a cup, tw = 0C

4. There is no heat interaction from outside

To find:

Mass of frozen water mw = ?

Solution:

According to laws of Thermodynamics, heat will flow from water to ice :

Heat lost by frozen water = Heat gained by ice ..... (1)

Qw = Qc

Here let's use the standard information for constants;

1.Specific heat of liquid water cw = 4190 J/kgK

2. Specific heat of ice cc = 2100 J/kgK

3. Heat of fusion cf = 3.34*10^5 J/kg ..... (2)

a) Calculate the heat lost by frozen water:

Qw = mw*cw*(tw-tc)

Qw = mw*4190*(0+10)

Qw = mw*41900   

b) Calculate the heat gained by ice:

Qc = (heat absorbed from -10C to 0C) + (heat of fusion)

Qc = mc*2100*(tw-tc) + mc*3.34*10^5

Qc = mc* (21000+334000)

Qc = 0.05*355000

Qc = 17750 J

From (1), (a), (b) we have,

mw*41900 = 17750

mw = 17750/41900

mw = 0.4236 kg

Answer:

Mass of water frozen = 0.4236 kg