Question

A 40-g block of ice is cooled to -70°C and is then added to 640 g of water in an 80-g copper calorimeter at a temperature of 23°C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to 0°C, melt, and then continue warming as water. (The specific heat of ice is 0.500 cal/g °C = 2,090 J/kg °C.)

Answer 1

The final temperature of the system is determined as 15 ⁰C.

How to calculate the final temperature of the system?

The final temperature of the system is calculated by applying the following formula as shown below;

Heat lost by the ice = heat gained by water + calorimeter

heat required to the temp of the ice + heat required to melt the ice + heat required to raise the temp = heat gained by water + calorimeter

0.04 kg x 2,090 J/kgC (0 + 70) + 334 J/g x 40 g + 40g x 4.186 J/gC (T - 0) = 640 g x 4.186 J/gC (23 - T) + 80 g x 0.385 J/gC (23 - T)

5,852 + 13,360 + 167.44T = 61,617.92 - 2,679.04 T + 708.4 - 30.8 T

2,877.28T = 43,114.32

T = 43,114.32 / 2,877.28

T = 15 ⁰C