Question

A cube of ice is taken from the freezer at -9.5 ∘C and placed in a 95-g aluminum calorimeter filled with 320 g of water at room temperature of 20.0 ∘C. The final situation is observed to be all water at 15.0 ∘C. The specific heat of ice is 2100 J/kg⋅C∘, the specific heat of aluminum is 900 J/kg⋅C∘, the specific heat of water is is 4186 J/kg⋅C∘, the heat of fusion of water is 333 kJ/Kg.

What was the mass of the ice cube?

Express your answer to two significant figures and include the appropriate units.

Answer 1

here,

the initial temperature of ice cube , T1 = - 9.5 degre C

the mass of alumunium calorimeter , m2 = 95 g

the mass of water in constainer , m3 = 320 g

the final temperature , Tf = 15 degree C

let the mass of ice cube be m1

using the principle of calorimetry

m1 * (Ci * ( 0 - T1) + Lf + Cw * ( Tf - 0)) = m2 * Ca * ( 20 - Tf) + m3 * Cw * ( 20 - Tf)

m1 * (2.100 * (9.5) + 334 + 4.186 * ( 15 - 0)) = 95 * 0.900 * ( 20 - 15) + 320 * 4.186 * ( 20 - 15)

solving for m1

m1 = 17.1 g

the mass of ice cube is 17 g