Question

A 40-g block of ice is cooled to

−72°C

and is then added to 590 g of water in an 80-g copper calorimeter at a temperature of 26°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.

a) final temperature of the system in degree celcius.

b)remaining mass of ice in grams.

Answer 1

specific heat of copper = 0.385 J/g.K

specific heat of water = 4.184 J/g.K

specific heat of ice = 2.09 J/g.K

Latent heat of fusion of water = 334 J/g

for 40 g ice to just melt from - 72 deg C to form water at 0 deg C

heat needed = 40*2.09*72+40*334 = 19379.2 J

heat available with copper and water = [(590*4.184)+(80*0.385)]*26 = 64983.36 J

so ice melts completely

so when ice turns to water at 0 deg C

balance heat

[(590*4.184)+(80*0.385)]*(26-T) = 19379.2 + 40*4.184*T

64983.36 - 2499.36T = 19379.2 + 167.36T

2499.36T + 167.36T = 64983.36 - 19379.2

2666.72T = 45604.16

solving,

T = 17.10 deg C