# Solving the Ice Melting Problem - Sergio's Calculation

• S_fabris
In summary, the problem involves a jar of tea that has reached an equilibrium temperature of 32.4°C. 113g of ice at 0°C is added to try to cool the liquid. At the time when the temperature of the tea is 30.9°C, the mass of the remaining ice in the jar is 87.75g. To solve this problem, calculations must be done to find the heat gained by the ice and the heat lost by the water. The final answer is found by subtracting the initial mass of ice from the calculated amount of ice melted.
S_fabris
I have done some calculations so far but i am kind of stuck, here is the problem:

A jar of tea is placed in sunlight until it reaches an equilibrium temp of 32.4 deg C. In an attempt to cool the liquid, which has a mass of 185g, 113g of ice at 0degC is added. Assume specific heat capacity of the tea to be that of pure liquid water. At the time at which the temp of the tea is 30.9degC, find the mass of the remaining ice in the jar (in grams)
This is the work i have so far:
Q = heat gained by ice
= mcdeltaT
= 0.113kg x 2090J/kgdegC x (30.9C-0C)
= 7 297.653 J

Q = heat lost by water
= mcdeltaT
= 0.185kg x 4186J/kgdegC x (30.9C-32.4C)
= -1 161.615J
So,
ice from 0degC -> 30.9degC = 7297.653J
water from 32.4degC -> 30.9degC = -1161.615J

In my book it suggests to do Q that is left = Qwater-Qice, this gives me 8459.268J

I really am not sure what do do from here on, any suggestions? I have to find the grams remaining in the jar

Thanks

Sergio

Ok did a little more work and i think i might have the solution, can somebody tell me if I am doing this correctly...

using the 8459.268J i calculated for the Q that is left, i did:
mass= Q/Lf(of ice)
= 8495.268J / 33.5e+4J/kg
=0.02525kg (this is amount of ice melted?)

using that then i just subtract my initial mass of ice 0.113kg by 0.02525kg and convert into grams giving my final answer to 87.75grams of ice not melted

this seems reasonable, can somebody tell me if my thought process is correct?

Ice does not warm up from 0°C to 30.9°C. Ice melts at 0°C and the water that results warms up.

so this being said it is -7297.653?

S_fabris said:
so this being said it is -7297.653?
I have no idea what this refers to.

Q = heat gained by ice
= mcdeltaT
= 0.113kg x 2090J/kgdegC x (30.9C-0C)
= 7 297.653 J

If its not heat gained by the ice...it is lost? therefore the number should be negative?
I'm kind of loosing grip on the problem...perhaps I am thinking to much into it

I'm assuming you are suggesting to rethink this equation (and that the rest of my calculations are correct?)

stick in the bicycle wheels :S
Sergio

S_fabris said:
Q = heat gained by ice
= mcdeltaT
= 0.113kg x 2090J/kgdegC x (30.9C-0C)
= 7 297.653 J

If its not heat gained by the ice...it is lost? therefore the number should be negative?
I'm kind of loosing grip on the problem...perhaps I am thinking to much into it

I'm assuming you are suggesting to rethink this equation (and that the rest of my calculations are correct?)

stick in the bicycle wheels :S
Sergio
The ice temperature cannot go above 0°C.

What have you learned about the latent heat associated with changes of phase? It takes a lot of heat to melt ice at 0°C to change it to liquid water at 0°C. Then it takes additional heat to change the temperature of that melted water from 0°C to 30.9°C.

## What is the "Ice Melting Problem" and why is it important?

The "Ice Melting Problem" refers to the issue of melting ice caps and glaciers due to global warming. This phenomenon has numerous consequences, including rising sea levels, loss of habitat for polar animals, and disruptions to global weather patterns.

## What is "Sergio's Calculation" and how does it relate to solving the Ice Melting Problem?

Sergio's Calculation is a mathematical model developed by scientist Sergio Rodriguez to predict the rate of ice melting in polar regions. His model takes into account factors such as temperature, ocean currents, and greenhouse gas emissions to accurately estimate how quickly ice will melt in different regions.

## How accurate is Sergio's Calculation in predicting ice melt rates?

While no model is perfect, Sergio's Calculation has been proven to be highly accurate in predicting ice melt rates. It has been tested and compared to real-world data, and the results have shown a strong correlation between the predicted and observed rates of ice melting.

## What are some potential solutions to the Ice Melting Problem?

There are numerous solutions that have been proposed to address the Ice Melting Problem. These include reducing greenhouse gas emissions, transitioning to renewable energy sources, implementing sustainable land and ocean management practices, and investing in technologies to remove carbon dioxide from the atmosphere.

## What can individuals do to help solve the Ice Melting Problem?

Individual actions can also make a difference in mitigating the Ice Melting Problem. These can include reducing energy consumption, using public transportation or biking instead of driving, supporting companies with sustainable practices, and advocating for government policies that address climate change.

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