# Kaplan vs GS answers: Cube of ice melting in water

#### bluefish9810

This question appeared in both Kaplan and Gold Standard, but they have contradicting answers...which is right?

Question: A block of ice floats in water. When it melts, what happens to the water level?

Kaplan answer: it will decrease because ice is less dense than water.

Gold Standard answer: it will remain the same because: [FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]
mg did not change
.[FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]The object displaces an amount of water equal to its weight when it is floating. Thus, if the object were to change state, since its mass remains constant, the level of the water would remain constant...

Gold Standard also says this:

imagine that you have a bucket of water. Take a styrofoam block and put it in the bucket. Of course, as soon as you put the styrofoam in the bucket, the level of the water will go up commensurate with the weight in volume of water displaced by the styrofoam.

Now take the styrofoam and crush it into a smaller volume and put it back in the bucket. Will the styrofoam push aside any more or less water than before? Of course, because the weight has not changed, the styrofoam has no more force to push aside more or less water. Thus the level of the water does not change.
So which is right? Kaplan or GS?

#### SFO-IST

10+ Year Member
7+ Year Member
This question appeared in both Kaplan and Gold Standard, but they have contradicting answers...which is right?

Question: A block of ice floats in water. When it melts, what happens to the water level?

Kaplan answer: it will decrease because ice is less dense than water.

Gold Standard answer: it will remain the same because: [FONT=Verdana, Arial, Helvetica, sans-serif][FONT=Verdana, Arial, Helvetica, sans-serif]

Gold Standard also says this:

So which is right? Kaplan or GS?

the water level remains unchanged. Are you sure you're reading the Kaplan question/answer correctly?

#### phltz

7+ Year Member
It doesn't even surprise me anymore when Kaplan is egregiously wrong about something like this.

#### loveoforganic

##### -Account Deactivated-
10+ Year Member
I'm pretty sure they're both right... They're talking about different situations. In Kaplan's situation, the buoyant object goes from floating to "sinking" when density changes. In GS's situation, the buoyant object remains floating.

#### phltz

7+ Year Member
I'm pretty sure they're both right... They're talking about different situations. In Kaplan's situation, the buoyant object goes from floating to "sinking" when density changes. In GS's situation, the buoyant object remains floating.

That doesn't even make sense.

#### loveoforganic

##### -Account Deactivated-
10+ Year Member
Ok... Let's stick to styrofoam.

Kaplan's situation is analogous to initially having a big airy ball of styrofoam floating in water and measuring the water level, then crushing every last bit of air out of the styrofoam ball so the ball sinks. Weight displaced initially, volume displaced next.

GS's situation is the same, but they don't crush the styrofoam enough to get it to sink - it remains floating in both conditions.

I'm open to correction if my interpretation of the first situation is off.

#### bluefish9810

So is the general consensus here that GS is correct? And that Kaplan isn't that accurate compared to GS? I just won 10 GS tests on ebay a couple of weeks ago for the price of 1 AAMC test so I thought I might as well try them out.

#### tartrate

10+ Year Member
Ok... Let's stick to styrofoam.

Kaplan's situation is analogous to initially having a big airy ball of styrofoam floating in water and measuring the water level, then crushing every last bit of air out of the styrofoam ball so the ball sinks. Weight displaced initially, volume displaced next.

GS's situation is the same, but they don't crush the styrofoam enough to get it to sink - it remains floating in both conditions.

I'm open to correction if my interpretation of the first situation is off.

That seems to be stretching the question too much. Also, how can you possibly have two different answers to the same question, provided you are answering the same question?

The question itself is simple: what happens to the water level when the ice melts?

It's much easier to think of it like this:

Situation 1: Measure X grams of water, freeze it, then add it to another container with a volume of Y.

Situation 2: Measure X grams of water, then add it to another container with a volume of Y.

How do their height levels compare?

In the first case, note that the amount of water displaced is equal to the weight of the ice. V_w*d_w*g=m_i*g. V_w=mass of ice/density of water.

In the second case, the volume changes by the volume of water you add, where V=mass of water/density of water.

Since you added the same mass X in both cases (mass of ice=X=mass of water), the volumes are equivalent, thus the water level remains the same.

Kaplan was probably just trying to test you on the concept of ice being less dense and thus occupying less volume than water, but confused themselves along the way.

#### loveoforganic

##### -Account Deactivated-
10+ Year Member
I misread part of the original post, then gave a wrong answer regardless of that

That seems to be stretching the question too much. Also, how can you possibly have two different answers to the same question, provided you are answering the same question?

The question itself is simple: what happens to the water level when the ice melts?

It's much easier to think of it like this:

Situation 1: Measure X grams of water, freeze it, then add it to another container with a volume of Y.

Situation 2: Measure X grams of water, then add it to another container with a volume of Y.

How do their height levels compare?

In the first case, note that the amount of water displaced is equal to the weight of the ice. V_w*d_w*g=m_i*g. V_w=mass of ice/density of water.

In the second case, the volume changes by the volume of water you add, where V=mass of water/density of water.

Since you added the same mass X in both cases (mass of ice=X=mass of water), the volumes are equivalent, thus the water level remains the same.

Kaplan was probably just trying to test you on the concept of ice being less dense and thus occupying less volume than water, but confused themselves along the way.

This explanation is correct Sorry for the confusion.

#### docelh

10+ Year Member
I think this is a stupid question because the answer is not known.

The part of the ice submerged in water will become more dense and should cause the water level to fall.

The part of the ice above water is not known, but it will contribute volume to the water and thereby raise it.

Without knowing the parts above water, it is difficult to say.

#### phltz

7+ Year Member
I think this is a stupid question because the answer is not known.

The part of the ice submerged in water will become more dense and should cause the water level to fall.

The part of the ice above water is not known, but it will contribute volume to the water and thereby raise it.

Without knowing the parts above water, it is difficult to say.

The answer is known. The water level does not change. This is a classic, standard question that intro-level physics students have been asked since shortly after Bernoulli figured this stuff out.

When the ice cube is floating, it displaces its weight in water. Once the ice cube melts, it develops the same density as water (because at that point it is water). This means it displaces its weight in water _and_ its volume in water, because those two values become the same. The amount of water displaced never changes, so the water level never changes.

#### SFO-IST

10+ Year Member
7+ Year Member
OP, you need to post the original questions, because there is still a chance that you have not interpreted Kaplan's question correctly (this is also an important component of the MCAT!). I would not take this one question, which may or may not be interpreted correctly, and label Kaplan as inferior to other testing.

#### bluefish9810

OP, you need to post the original questions, because there is still a chance that you have not interpreted Kaplan's question correctly (this is also an important component of the MCAT!). I would not take this one question, which may or may not be interpreted correctly, and label Kaplan as inferior to other testing.

Here is the question for Kaplan:

A container is filled with an ice-water mixture to a hieght of 15cm. Another substance is added, and a transfer of heat causes the water-ice mixture to rise H cm in height. Which of the following could have caused this rise?

A. Cu at 0C
B. Hg at -2.5C
C. Fe at 75C
D. O2 at 15C

Kaplan Explanation: As heat is transfered TO the bath, ice begins to melt. Since ice = smaller density than water, its melting will DECREASE the volume of the bath. Here the height of the bath increases, so we are not melting ice, but freezing water. Heat must be transferred FROM the bath.

#### SFO-IST

10+ Year Member
7+ Year Member
Here is the question for Kaplan:

A container is filled with an ice-water mixture to a hieght of 15cm. Another substance is added, and a transfer of heat causes the water-ice mixture to rise H cm in height. Which of the following could have caused this rise?

A. Cu at 0C
B. Hg at -2.5C
C. Fe at 75C
D. O2 at 15C

Kaplan Explanation: As heat is transfered TO the bath, ice begins to melt. Since ice = smaller density than water, its melting will DECREASE the volume of the bath. Here the height of the bath increases, so we are not melting ice, but freezing water. Heat must be transferred FROM the bath.

I had to read this answer twice to understand that the first sentence of the answer is not talking about the situation described in the question. I'm not sure if that also confused you, but in this case, what's happening is that the ice is NOT melting, but freezing. Since H2O has more volume as ice instead of water, you get a rise in the mixture when you add this mystery substance that sucks up the heat in the container. It must have been below freezing in order to create ice, so B is the only answer.

A crappy explination from Kaplan though. Wow, how confusing to start the answer with the opposite of what's going on here without clarifying that it's the opposite. kaplan!

Last edited:

#### phltz

7+ Year Member
Here is the question for Kaplan:

A container is filled with an ice-water mixture to a hieght of 15cm. Another substance is added, and a transfer of heat causes the water-ice mixture to rise H cm in height. Which of the following could have caused this rise?

A. Cu at 0C
B. Hg at -2.5C
C. Fe at 75C
D. O2 at 15C

Kaplan Explanation: As heat is transfered TO the bath, ice begins to melt. Since ice = smaller density than water, its melting will DECREASE the volume of the bath. Here the height of the bath increases, so we are not melting ice, but freezing water. Heat must be transferred FROM the bath.

This is a typical terrible Kaplan question. It's confusingly written, doesn't adequately explain the situation they're proposing, and gets the science wrong. The only way for their explanation to make sense is by assuming that extra stuff is happening that they never mention. There will be more questions like this, I promise you.

The container holds an ice-water mixture. Is the ice floating in the water? Or is it a glass of ice cubes that are touching the bottom, only partially supported by buoyant force? These are two very different situations, and will give different results. Either seems a reasonably interpretation of the question stem. Unfortunately, the description in the question stem doesn't make it clear.

As it turns out, the only way their explanation could make sense is if the ice is forced below its normal floating level - perhaps it might be pushed below the surface by the experimenter. Only in that case will freezing more water onto the ice cause the water level to rise.

Of all of the ways that you can interpret this poorly written ****-show of a question, the way they wanted you to read it was the one that involves the experimenter actively doing stuff that they don't mention. This should be an embarrassment, but instead it's sadly typical. If this is the kind of work that Kaplan's central office puts out, I shudder to think at what the slack-jawed idiots in their field-offices are like.

#### BerkReviewTeach

##### Company Rep & Bad Singer
Vendor
10+ Year Member
This question appeared in both Kaplan and Gold Standard, but they have contradicting answers...which is right?

Question: A block of ice floats in water. When it melts, what happens to the water level?

Kaplan answer: it will decrease because ice is less dense than water.

Gold Standard answer: it will remain the same because

Funny, because that same question is in the BR materials (and no doubt EK and PR as well). The BR answer matches with GS.

If you have water in a graduated cylinder up to an observed height, then adding a 10-g ice cube will cause the water to rise to the exact same point as adding 10-g of water at the same temperature. Keep in mind that the ice cube will be partially exposed (about 9%) and mostly submerged (about 91%). When that ice cube melts, it becomes the same material as the surrounding solution (assuming it's pure water) and takes up less volume, resulting in the same height but without anything sticking out of the soultion like before.

So, while the overall volume of the system goes down, the height of the water remains the same.

You know, it's a lot harder to explain this concept than I expected.

#### LaurenMCAT

##### Elite Kaplan Instructor
bluefish9810 -

This is a GREAT topic to discuss! Buoyancy tends to be a difficult subject for a lot of students, and as a former Kaplan MCAT student and now instructor, I like this problem because it highlights some critical concepts

Unfortunately, I'm not sure where you're looking in your Kaplan materials, because everything I've read AND taught (yesterday in class, in fact!) says that:

...the water level before the ice cube melts and after the ice cube melts...IS EXACTLY THE SAME

(Think about Conservation of Mass AND net forces: The mass of the ice cube does NOT change as it melts...and because the ice and the melted water both float either on top or within the fluid, we have a net force of zero: the downward force of gravity acting on the ice is equal to the upward buoyant force in both cases...and the displaced water in the cup doesn't increase or decrease, so our water level stays EXACTLY the same! I recommend you draw a free body diagram.)

This is inline with the conclusions made by other prep materials. If you'd like, you're welcome to private message me with the exact source of your Kaplan reference.

Cheers!

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