# Homework Help: Fusion of Ice

1. Jan 15, 2017

### Biker

1. The problem statement, all variables and given/known data
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

2. Relevant equations
q = M C dT
dH = n (molar dH)

3. The attempt at a solution
I am going to assume both ice are at exactly 0 C and they only calculated until the

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 cant use this equation.. Secondly C isnt 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

Last edited: Jan 15, 2017
2. Jan 15, 2017

### haruspex

Not if you interpret that as including the heat required to bring the ice to melting point first.

3. Jan 15, 2017

### Biker

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. Jan 15, 2017

### haruspex

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. Jan 16, 2017

### Biker

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. Jan 16, 2017

### haruspex

See the second paragraph in post #4.

7. Jan 16, 2017

### Biker

Ummm So you agree on the answer being More ice equal less temperature drop?
It says
A:B 1 : 2

8. Jan 16, 2017

### haruspex

I'm saying that I think the question was intended to say that "Heat per unit mass required to fuse both cubes are equal"