Question

A 24 g block of ice is cooled to −63^{◦}C. It is added
to 572 g of water in a 98 g copper calorimeter at a temperature of
30^{◦}C.

Find the final temperature. The specific heat of copper is 387
J/kg ·^{◦}C and of ice is 2090 J/kg ·^{◦}C. The
latent heat of fusion of water is 3.33 × 105 J/kg and its specific
heat is 4186 J/kg·^{◦}C.

Answer in units of ^{◦}C.

Answer #1

For the ice to reach 0 degrees, you will need

63 * 2090 * 0.024 J = 3160.08

The latent heat needed to melt the ice is 333 J / g.

So to melt the ice, you will need

333 * 24= 7992 J

Assume final temperature = x degC

Specific heat of water is 4.186 J / g degC.

So heat applied to ice will be x * 4.186 * 24

Total heat energy applied = 3160.08 + 7992 + 1004.64x

Heat from water = (30-x) * 4.18 * 572= 71728 - 2390.96x

Specific heat of copper is 0.387J / g degC.

Heat from copper = (30-x) * 0.387 * 98 = 1137.78- 37 .926x

Heat gained = heat loss

3160.08+ 7992 + 1004.64x = 71728 - 2390.96x + 1137.78- 37.926x

On solving we get

x =~ 25

So final temperature is 25 degC.

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