Exploring the Ratio of Melting Ice Cubes

In summary, the answer to this question is that the two cubes have different masses and as a result the temperature drop is lower when the ice is melted incup A.
  • #1
Biker
416
52

Homework Statement


The following chart shows the temperature before and after Melting Ice. (A, B) have the same amount of water. If the heat required to fuse both cube are equal. The ratio between the two cubes mass:
Cup Before After
A 25 21
B 25 23

A :B
1) 2: 1
2) 1:1
3) 1:2
4) 1: 4

Homework Equations


q = M C dT
dH = n (molar dH)

The Attempt at a Solution


I am going to assume both ice are at exactly 0 C and they only calculated until the [/B]
This question came in an exam two years ago and it is confusing me a lot.
"Heat required to fuse both cubes are equal" Which implies that the two cubes must have the same mass.
But there is a difference in the temperature so the mass must not be the same
I used this equation.
n (molar dH) = M(water) C dT
for both a and b which means
that The ice cube placed in A has twice the mass of ice cube placed in B.

They chosed 3 as an answer by the following way
q = m(a) c dT
q = m(b) c dT
and by the statement of "Heat required to fuse both cubes are equal" you get Mb:Ma 2:1
But there is a couple of problems here.
First if we assume that they placed it at 0 C and then left both cups until they reach equilibrium. You dT is not a common factor between the ice and water so you can't use this equation.. Secondly C isn't the same you can make an approximation to calculate it which shows that c is not the same. So The question is poorly made.A real solution would make an expression of the heat required to fuse it to water then raise that amount of water(Ice after melted) temperature to the equilibrium temperature. Which would be close to 1:1 because the amount of heat needed to raise to equilibrium temperature is negligible
 
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  • #2
Biker said:
Heat required to fuse both cubes are equal" Which implies that the two cubes must have the same mass.
Not if you interpret that as including the heat required to bring the ice to melting point first.
 
  • #3
haruspex said:
Not if you interpret that as including the heat required to bring the ice to melting point first.
What so ever, Didn't it say same heat used to fuse? so If I take te same heat from each cup the final temperature should be equal
 
  • #4
Biker said:
Didn't it say same heat used to fuse?
Sure, but the process of melting the ice involved bringing it to 0C first. The cost of landing a person on the moon includes the cost of getting them into orbit around it.

Anyway, given the stated answer, it looks like they meant the heat per unit mass required was the same. So, yes, a very sloppy question.
 
  • #5
haruspex said:
Sure, but the process of melting the ice involved bringing it to 0C first. The cost of landing a person on the moon includes the cost of getting them into orbit around it.

Anyway, given the stated answer, it looks like they meant the heat per unit mass required was the same. So, yes, a very sloppy question.
Sure thing that I have to bring it to zero( I would need the initial value of temperature). What I am saying is check their solution to this problem. It is up there in The OP.
Their solution says that B has more ice in it thus the decrease in temperature is lower
 
  • #6
Biker said:
What I am saying is check their solution to this problem. It is up there in The OP.
See the second paragraph in post #4.
 
  • #7
haruspex said:
See the second paragraph in post #4.
Ummm So you agree on the answer being More ice equal less temperature drop?
It says
A:B 1 : 2
 
  • #8
Biker said:
Ummm So you agree on the answer being More ice equal less temperature drop?
It says
A:B 1 : 2
I'm saying that I think the question was intended to say that "Heat per unit mass required to fuse both cubes are equal"
 

FAQ: Exploring the Ratio of Melting Ice Cubes

1. What is the purpose of exploring the ratio of melting ice cubes?

The purpose of exploring the ratio of melting ice cubes is to gain a better understanding of the factors that affect the melting rate of ice, such as temperature, surface area, and material of the ice cube. This information can then be used to make predictions and improve processes in various industries, such as refrigeration and climate control.

2. How do you conduct an experiment to explore the ratio of melting ice cubes?

To conduct an experiment, first gather materials such as ice cubes, a thermometer, a timer, and various containers to hold the ice cubes. Then, measure and record the initial temperature of the ice cubes and place them in the containers. Observe and record the melting rate of the ice cubes over a set period of time, making note of any variables that may affect the results. Finally, analyze the data to determine the ratio of melting ice cubes.

3. What factors can affect the ratio of melting ice cubes?

The ratio of melting ice cubes can be affected by various factors, such as temperature, surface area, and material of the ice cube. Higher temperatures will cause ice to melt faster, while a larger surface area allows for more heat transfer and therefore a faster melting rate. The material of the ice cube can also play a role, as some materials may have a lower melting point or better insulation properties.

4. How can the results of exploring the ratio of melting ice cubes be applied?

The results of exploring the ratio of melting ice cubes can be applied in many ways, such as improving refrigeration and freezing processes, predicting the effects of climate change on ice formations, and understanding the impact of temperature on food and drink storage. This information can also be used to develop more efficient and sustainable cooling methods.

5. Are there any limitations to exploring the ratio of melting ice cubes?

One limitation of exploring the ratio of melting ice cubes is that it is a simplified experiment and may not accurately reflect real-world scenarios. Factors such as air flow, humidity, and external pressure can also affect the melting rate of ice. Additionally, the materials and methods used in the experiment may not be able to replicate all possible scenarios, so the results should be interpreted with caution.

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