Question

A 40-g block of ice is cooled to −70°C and is then added to 570 g of water in an 80-g copper calorimeter at a temperature of 22°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.)

Tf= _____ °C

m ice, final = ______ g

Answer 1

DATA:

SOLUTION

Assuming that all ice melts. Then the final temperature will be positive . If all ice melts, then the energy is conserved. So:

In this problem, equation (1) must be written as:

Where:

is the heat for ice from (solid) to (solid). Therefore:

or

is heat for ice from (solid) to (liquid); or:

is the heat for ice from (liquid) to the final temperature of system ; or

is the heat released by liquid water from to the final temperature of system ; or

is the heat released by copper from to the final temperature of system ; or

Now, replacing equations (3), (4), (5) , (6), (7) and (8) into equation (2) we have:

Replacing data given values into equation above:

Isolating we obtain:

Because then, all ice melts.