# Isaac physics help - latent heat.

Hi,
I’ve been stuck on this question for a bit now.

A mass of 0.35kg ice at -15∘C is lowered into an insulated beaker containing water at 59∘C
. What is the minimum mass of water at this temperature needed in the beaker to achieve a final temperature of 0.0∘C?

From previous parts of the question I worked out that it required 10657.5J to heat the ice to 0 degrees, it then required an additional 117250J to melt the ice.

I think I need to use Q=mc delta T with the smallest value of Q that I can but I’m not sure what value of Q I need as I tried 10657.5 and got a mass of 0.043kg but it said that although that results in 0degrees it isn’t the smallest mass.

Any help would be much appreciated
Original post by Snoozinghamster
Hi,
I’ve been stuck on this question for a bit now.

A mass of 0.35kg ice at -15∘C is lowered into an insulated beaker containing water at 59∘C
. What is the minimum mass of water at this temperature needed in the beaker to achieve a final temperature of 0.0∘C?

From previous parts of the question I worked out that it required 10657.5J to heat the ice to 0 degrees, it then required an additional 117250J to melt the ice.

I think I need to use Q=mc delta T with the smallest value of Q that I can but I’m not sure what value of Q I need as I tried 10657.5 and got a mass of 0.043kg but it said that although that results in 0degrees it isn’t the smallest mass.

Any help would be much appreciated

There is no description of the final state of matter in the beaker... I guess you don't need to consider the energy used to melt the ice - a beaker containing ice at 0.0 degrees is sufficient to answer the question.
Original post by Joinedup
There is no description of the final state of matter in the beaker... I guess you don't need to consider the energy used to melt the ice - a beaker containing ice at 0.0 degrees is sufficient to answer the question.

That’s what I thought, the values I used came from just the energy needed to heat the ice to 0 degrees so I have 0 degree ice in 0 degrees water.
The hint at the end has said think about the energy transferred as ice goes to water and vice Versa. But I can’t think of any way of using that info.

Thanks again
Original post by Snoozinghamster
Hi,
I’ve been stuck on this question for a bit now.

A mass of 0.35kg ice at -15∘C is lowered into an insulated beaker containing water at 59∘C
. What is the minimum mass of water at this temperature needed in the beaker to achieve a final temperature of 0.0∘C?

From previous parts of the question I worked out that it required 10657.5J to heat the ice to 0 degrees, it then required an additional 117250J to melt the ice.

I think I need to use Q=mc delta T with the smallest value of Q that I can but I’m not sure what value of Q I need as I tried 10657.5 and got a mass of 0.043kg but it said that although that results in 0degrees it isn’t the smallest mass.

Any help would be much appreciated

Figured it out?
Original post by I'msoPi
Figured it out?

Yeh, in the end my teacher proudly told me she had managed all but one question, that question🤦*♀️ but then we had the sudden realisation that the hot water turned into ice as that released more energy. From there it was ok.

Edit: and yes, it took 7 months for us to solve it!
(edited 5 years ago)
Original post by Snoozinghamster
Yeh, in the end my teacher proudly told me she had managed all but one question, that question🤦*♀️ but then we had the sudden realisation that the hot water turned into ice as that released more energy. From there it was ok.

Edit: and yes, it took 7 months for us to solve it!

Ahaha can't believe you responded even though this was from months ago. I'm doing that question now so lemme give it another crack knowing that it turns to ice
Original post by I'msoPi
Ahaha can't believe you responded even though this was from months ago. I'm doing that question now so lemme give it another crack knowing that it turns to ice

Oh and good luck with it.
(edited 5 years ago)
Original post by Snoozinghamster
Oh and good luck with it.

Stream? ergh my brain is actually too frazzled at this point to complete this question lol
Original post by I'msoPi
Stream? ergh my brain is actually too frazzled at this point to complete this question lol

Stream-Show on twitch someone gaming

If you try again and It doesn’t work let me know and I’ll try and explain it better
Original post by Snoozinghamster
Stream-Show on twitch someone gaming

If you try again and It doesn’t work let me know and I’ll try and explain it better

Ah yeah I thought it was something on twitch. Thermal physics is killing me softly, would you mind explaining it
Original post by I'msoPi
Ah yeah I thought it was something on twitch. Thermal physics is killing me softly, would you mind explaining it

I can certainly try.

When ice melts into water that takes energy, when the same mass of water freezes that releases the same amount of energy.

So here we have ice at a cold temperature so we need to raise it up to 0 degrees, we can work out how much energy is needed by Q=mc \delta T. This is the energy we need.

The water is at 59 degrees so we need to work out how much energy is released in cooling it to zero. (This will be in terms of m)

Then the bit that I didn’t know to do.
You need to work out the energy released in freezing the water using the latent heat of fusion times mass.

The energy needed to warm the ice = the total energy released.

From here you just rearrange to find m.

Hoops that helps
Original post by Snoozinghamster
I can certainly try.

When ice melts into water that takes energy, when the same mass of water freezes that releases the same amount of energy.

So here we have ice at a cold temperature so we need to raise it up to 0 degrees, we can work out how much energy is needed by Q=mc \delta T. This is the energy we need.

The water is at 59 degrees so we need to work out how much energy is released in cooling it to zero. (This will be in terms of m)

Then the bit that I didn’t know to do.
You need to work out the energy released in freezing the water using the latent heat of fusion times mass.

The energy needed to warm the ice = the total energy released.

From here you just rearrange to find m.

Hoops that helps

Yay I just got it now thanks!! Although I don't fully understand why I didn't have to use the energy required to melt the ice (the latent heat one) but i'm assuming it's just because it doesn't actually melt?
Original post by I'msoPi
Yay I just got it now thanks!! Although I don't fully understand why I didn't have to use the energy required to melt the ice (the latent heat one) but i'm assuming it's just because it doesn't actually melt?

Yeh the ice doesn’t melt as we want the minimum energy required to get it to 0 degrees and it would require additional energy to melt the ice
Original post by Snoozinghamster
Yeh the ice doesn’t melt as we want the minimum energy required to get it to 0 degrees and it would require additional energy to melt the ice

Ahhhh okay thanks again for the help. I'm in a good mood now that this is finished lol
can you help me with the maximum mass?
I am not sure how I did it but I was also stuck on this question for ages.

For the MAXIMUM mass:
I found the energy needed for ice to melt (Q = m*c*deltaT) = 10675.5J
Then I found the latent heat of fusion for the ice to melt fully (Q = m*l) and added those values together for the total amount of energy required to melt the ice. (I think that is what it is but I did it and it seemed to work)

For the water I did the same thing as before with the minimum mass, work out how much energy is released in cooling it to zero. (This will be in terms of m)
But I didn't work out the energy released in freezing the water (the latent heat).

As before the energy needed to warm the ice = the total energy released.

And then rearrange for m.

Sorry I couldn't explain how or why this gets the correct answer.
(edited 3 years ago)
To find the minimum mass of water for the mixture to reach zero:
(energy needed to cool water from 59°C to 0°C) + (energy released in freezing this water) = (energy to heat the ice from -15°C to 0°C)
This forms the equation:
(m*4180*59) + (m*3.35e5) = (0.35*2030*15)
rearrange for m:
m = (0.35*2030*15) / ((4180*59) + (3.35e5))

To find the maximum mass of water for the mixture to reach zero:
(energy needed to cool water from 59°C to 0°C) = (energy needed to heat ice from -15°C to 0°C) + (energy needed to melt the ice)
This forms the equation:
(m*4180*59) = (0.35*2030*15) + (0.35*3.35e5)
rearrange for m:
m = ((0.35*2030*15) + (0.35*3.35e5)) / (4180*59)

This thread helped me understand this question and this is my way of thinking about it.
(edited 1 year ago)