An insulated beaker with negligible mass contains liquid wat

An insulated beaker with negligible mass contains liquid water with a mass of 0.350 kg and a temperature of 61.2 C .

How much ice at a temperature of -11.5 C must be dropped into the water so that the final temperature of the system will be 36.0 C ?

Take the specific heat of liquid water to be 4190 J/kgK , the specific heat of ice to be 2100 J/kgK , and the heat of fusion for water to be 3.34×10⁵J/kg .

Solution

mass of water , mw = 0.295 kg

temprature , Tw = 61.7 degree C

initial temprature of ice , Ti = - 14 degree C

final temprature , Tf = 40 degree C

let the mass of ice be mi

heat lost by water = heat energy gained by ice

mw * Cw * ( Tw - Tf) = mi * Ci * (0 - Ti) + mi * Lf + mi * Cw * ( Tf - 0)

0.350 * 4186 * ( 61.2 - 36) = mi * ( 2100 * 11.5 + 334000 + 4186 * 36)

mi = 0.07255 kg

the mass of ice dropped is 0.07255 kg