Final Temperature of Drink After Adding Ice Cubes

In summary, four 20 g ice cubes each at a temperature of -3°C are dropped into the tumbler, which results in a final temperature of -3.33*105 J/kg.
  • #1
kachilous
15
0

Homework Statement


A 25 g glass tumbler contains 350 mL of water at 24°C. If four 20 g ice cubes each at a temperature of -3°C are dropped into the tumbler, what is the final temperature of the drink? Neglect thermal conduction between the tumbler and the room.

Homework Equations


Q = mcT
Q = mLf (energy required to melt a substance of mass m)

The Attempt at a Solution


Here are all the known variables:
massw = .35kg
c (specific heat for water) = 4186 J/kg * C
Twater,initial = 24 C
massice = 4*20g = .08kg
Lf = 3.33*105 J/kg
Tice,initial = -3 C
Tf = ?

First I can use Q = mcT to see if all the ice will get melted by the water
Q = (.35kg)*(4186 J/kgC)*(24C) = 35162.4 J
m = Q/Lf = (35162.4 J) / (3.33*105 J/kg) = .105592
Since the total mass of the ice is .08, then all the ice will get melted.

Now we can apply conservation of energy to find the final temperature.
massw*c*(Twater,initial - Tf) = massice*Lf + massice*c*(Tf-Tice,initial)

Plugging in all my variables and solving I get 4.18 C which is incorrect.
My math could be wrong but I don't believe it is.
Could anyone provide any insight on what I am doing wrong?
 
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  • #2
The initial ice goes to the final water in three steps: Increase the temperature of the ice; melt the ice; increase the temperature of the resulting water.
 
  • #3
I'm still confused. Here are the three steps you mentioned.

(1) Increase the temperature of the ice: Q = mice*cice*(Tf-Tice,initial)
(2) Melt the ice: Q = mice*Lfusion,water
(3) Increase temperature of water: Q = mwater,initial*cwater*(Twater,initial*Tf)

And then the equation would be: (1) + (2) = (3)

Is this the correct setup?
 
  • #4
kachilous said:
I'm still confused. Here are the three steps you mentioned.

(1) Increase the temperature of the ice: Q = mice*cice*(Tf-Tice,initial)
(2) Melt the ice: Q = mice*Lfusion,water
(3) Increase temperature of water: Q = mwater,initial*cwater*(Twater,initial*Tf)

And then the equation would be: (1) + (2) = (3)

Is this the correct setup?
Not exactly. The ice is warmed up to the final temperature and the 350 ml of water is cooled down to the final temperature. The energy added to the ice equals the energy lost by the water.

Just thinking about the warming of the ice, here are the three steps:
(1) Raise the temperature of the ice from its initial temperature to the melting point.
(2) Melt the ice.
(3) Raise the temperature of the melted ice (water, of course) from the melting point to the final temperature.

Give it another shot.
 
  • #5
I figured it out. Thank you!
 

FAQ: Final Temperature of Drink After Adding Ice Cubes

What is conservation of heat energy?

Conservation of heat energy is a fundamental principle in physics that states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

Why is conservation of heat energy important?

Conservation of heat energy is important because it helps us understand and predict how energy is transferred and used in various processes and systems, such as in the Earth's atmosphere and in our daily lives. It also helps us conserve energy and reduce waste.

How is heat energy conserved?

Heat energy can be conserved by utilizing efficient insulation, reducing heat loss through conduction, convection, and radiation, and using renewable energy sources that do not deplete natural resources.

What is an example of conservation of heat energy in action?

An example of conservation of heat energy is the use of a thermos to keep a hot drink warm. The thermos is designed with efficient insulation to prevent heat loss, conserving the heat energy of the drink inside for a longer period of time.

What are the implications of not conserving heat energy?

If heat energy is not conserved, it can lead to wastage of energy, increased energy costs, and negative impacts on the environment, such as air pollution and climate change. It can also result in inefficient use of resources and energy shortages in the long run.

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