Phase change Melting ice with hot tea.

In summary, the problem involves pouring 175 cm3 of hot tea at 87°C into a paper cup containing 80 g of crushed ice at 0°C. Calculating the final temperature of the mixture requires taking into account the heat loss from the tea, the heat needed to melt the ice, and the heat gained by the melted ice-water. By setting up equations and solving for the final temperature, it is determined that the final temperature of the "ice tea" is 7.3°C.
  • #1
lwaiyipl
4
0

Homework Statement



175 cm3 of hot tea at 87°C are poured into a very thin paper cup with 80 g of crushed ice at 0°C. Calculate the final temperature of the "ice tea". (Hint: think about two processes: melting the ice into liquid and, maybe, warming the liquid.)

Homework Equations



Q=mc(deltaT)
Q=mL

The Attempt at a Solution



First, I calculated the heat loss by the tea:
Q1=(.0175)(4186)(87)=63731.9J

Then the heat needed to melt the ice:
Q2=(0.08)(33.5e4)=26800J

Heat gain by the melted ice-water
Q3=(.08)(4186)(87)=29134.6J

Then Q(final)= Q1-Q2-Q3
=7797.34J

Set it equal to the entire system
7797.34J=(0.255)(4186)(T)

My answer is 7.3 deg Celsius, which is wrong. I can't seem to find what I did wrong!
Please help! Thanks.
 
Last edited:
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  • #2
Hi lwaiyipl, welcome to PF.
Since Q1> Q2, temperature of the tea does not reach zero degree. So rewrite the first and third equation taking θ as the final temperature of the mixture.
 
  • #3
Hey rl.bhat, thanks for the reply. But I still don't quite get it. If I make the final temperature as a variable, θ, then I will get θ=102.437 deg Celsius, which is hotter than the original 87 deg.
ARRGH, I am pulling my hairs out for this problem!
 
Last edited:
  • #4
In Q1 temperature will be (87- θ)
In Q3 temperature will be θ and mass of the mixture will be ...?
 
  • #5
I see that the work I showed at the first post is incorrect, it's 0.175 instead of 0.0175.
So
Q1=(0.175)(4186)(87-θ)

Q2=(0.08)(33.5e4)

Q3=(0.175+0.08)(4186)(θ-0)

Am I setting it up correctly?
I have a question about Q3, why do we add the tea with the melted ice-water? Aren't we calculating for the amount of heat needed to raise the melted ice-water from 0 deg to θ?
 
  • #6
Yes. You are right.
 
  • #7
Thanks rl.bhat. Sorry about late reply. I got the answer now!
 

1. What is the phase change that occurs when melting ice with hot tea?

The phase change that occurs is from solid to liquid, also known as melting or fusion.

2. Why does melting ice with hot tea occur?

This occurs because the temperature of the hot tea is higher than the melting point of ice, causing the ice to absorb heat and change from solid to liquid.

3. Does the amount of ice affect the phase change when melting with hot tea?

Yes, the amount of ice will affect the phase change. The more ice there is, the longer it will take to melt and the more heat will be required.

4. Is there a difference between melting ice with hot tea versus cold tea?

Yes, there is a difference. When melting ice with hot tea, the ice will melt faster due to the higher temperature of the tea. Cold tea will still cause the ice to melt, but at a slower rate.

5. Can the phase change of melting ice with hot tea be reversed?

Yes, the phase change can be reversed. If the ice water is cooled down below its freezing point, it will turn back into ice. This is referred to as freezing or solidification.

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