Question

A 25 g ice cube at -15.0^oC is placed in 169 g of water at 48.0^oC. Find the final temperature of the system when equilibrium is reached. Ignore the heat capacity of the container and assume this is in a calorimeter, i.e. the system is thermally insulated from the surroundings. Give your answer in ^oC with 3 significant figures.

Specific heat of ice: 2.090 J/g K

Specific heat of water: 4.186 J/g K

Latent heat of fusion for water: 333 J/g

Answer 1

here,

mass of ice cube , m1 = 25 g

the initial temperature of ice cube , T1 = - 15 degree C

mass of water , m2 = 169 g

the initial temperature of water , T2 = 48 degree C

let the final equilibrium temperature be Tf

using principle of calorimetry

m1 * ( Ci * ( 0 - T1) + Lf + Cw * ( Tf - 0)) = m2 * ( Cw * ( T2 - Tf))

25 * ( 2.09 * ( 0 - (-15)) + 333 + 4.86 * ( Tf - 0)) = 169 * 4.186 * ( 48 - Tf)

solving for Tf

Tf = 29.98 degree C

the final temperature is 29.98 degree C