# 6.6 Phase change and latent heat  (Page 3/9)

 Page 3 / 9

## Calculate final temperature from phase change: cooling soda with ice cubes

Three ice cubes are used to chill a soda at $\text{20º}\text{C}$ with mass . The ice is at $0º\text{C}$ and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored. Assume the soda has the same heat capacity as water. Find the final temperature when all ice has melted.

Strategy

The ice cubes are at the melting temperature of $0º\text{C}$ . Heat is transferred from the soda to the ice for melting. Melting of ice occurs in two steps: first the phase change occurs and solid (ice) transforms into liquid water at the melting temperature, then the temperature of this water rises. Melting yields water at $0º\text{C}$ , so more heat is transferred from the soda to this water until the water plus soda system reaches thermal equilibrium,

${Q}_{\text{ice}}=-{Q}_{\text{soda}}\text{.}$

The heat transferred to the ice is ${Q}_{\text{ice}}={m}_{\text{ice}}{L}_{\text{f}}+{m}_{\text{ice}}{c}_{\text{W}}\left({T}_{\text{f}}-0º\text{C}\right)$ . The heat given off by the soda is ${Q}_{\text{soda}}={m}_{\text{soda}}{c}_{\text{W}}\left({T}_{\text{f}}-\text{20º}\text{C}\right)$ . Since no heat is lost, ${Q}_{\text{ice}}=-{Q}_{\text{soda}}$ , so that

${m}_{\text{ice}}{L}_{\text{f}}+{m}_{\text{ice}}{c}_{W}\left({T}_{\text{f}}-0º\text{C}\right)=-{m}_{\text{soda}}{c}_{W}\left({T}_{\text{f}}-\text{20º}\text{C}\right)\text{.}$

Bring all terms involving ${T}_{\text{f}}$ on the left-hand-side and all other terms on the right-hand-side. Solve for the unknown quantity ${T}_{\text{f}}$ :

${T}_{\text{f}}=\frac{{m}_{\text{soda}}{c}_{W}\left(\text{20º}\text{C}\right)-{m}_{\text{ice}}{L}_{\text{f}}}{\left({m}_{\mathrm{soda}}+{m}_{\text{ice}}\right){c}_{W}}\text{.}$

Solution

1. Identify the known quantities. The mass of ice is and the mass of soda is .
2. Calculate the terms in the numerator:

and

3. Calculate the denominator:
4. Calculate the final temperature:

Discussion

This example illustrates the enormous energies involved during a phase change. The mass of ice is about 7 percent the mass of water but leads to a noticeable change in the temperature of soda. Although we assumed that the ice was at the freezing temperature, this is incorrect: the typical temperature is $-6º\text{C}$ . However, this correction gives a final temperature that is essentially identical to the result we found. Can you explain why?

We have seen that vaporization requires heat transfer to a liquid from the surroundings, so that energy is released by the surroundings. Condensation is the reverse process, increasing the temperature of the surroundings. This increase may seem surprising, since we associate condensation with cold objects—the glass in the figure, for example. However, energy must be removed from the condensing molecules to make a vapor condense. The energy is exactly the same as that required to make the phase change in the other direction, from liquid to vapor, and so it can be calculated from $Q={\text{mL}}_{\text{v}}$ .

## Real-world application

Energy is also released when a liquid freezes. This phenomenon is used by fruit growers in Florida to protect oranges when the temperature is close to the freezing point $\left(0º\text{C}\right)$ . Growers spray water on the plants in orchards so that the water freezes and heat is released to the growing oranges on the trees. This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
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?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
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Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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