Exploring the Ratio of Melting Ice Cubes

[Biker]

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

 

[haruspex]

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.

 

[Biker]

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

 

[haruspex]

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.

 

[Biker]

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

 

[haruspex]

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.

 

[Biker]

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

 

[haruspex]

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"