Question

An ice cube (of mass 5 gm ), at a temperature of 0 23 c , is dropped into a lake whose temperature is 0 27

c. After equilibrium is established, what is the change: in the entropy of the universe nearest to?

Answer 1

Explanation:

As far as solving this problem goes, it is very importantthat you do not forget to account for the phase changeunderwent by the solid water at 0∘C to liquid at 0∘C.

The heat needed to melt the solid at its melting point will come from the warmer water sample. This means that you have

q1+q2=−q3 (1), where

q1 - the heat absorbed by the solid at 0∘C

q2 - the heat absorbed by the liquid at 0∘C

q3 - the heat lost by the warmer water sample

The two equations that you will use are

q=m⋅c⋅ΔT , where

q - heat absorbed/lost

m - the mass of the sample

c - the specific heat of water, equal to 4.18Jg∘C

ΔT - the change in temperature, defined as final temperature minus initial temperature

and

q=n⋅ΔHfus , where

q - heat absorbed

n - the number of moles of water

ΔHfus - the molar heat of fusion of water, equal to 6.01 kJ/mol

Use water's molar mass to find how many moles of water you have in the 100.0-g sample

100.0g⋅1 mole H2O18.015g=5.551 moles H2O

So, how much heat is needed to allow the sample to go from solid at 0∘C to liquid at 0∘C?

q1=5.551