Thermodynamics Homework: Solving for Final Temperature and Heat Exchange

• fluvly
In summary, the problem involves a container with thermally insulating walls containing two parts, A and B, with water at 15.6 degrees Celsius and ice at 0 degrees Celsius separated by an insulating plate. The question asks for the final temperature of the system and the heat exchanged between the water and ice. The solution involves using the equations Q=mc(Tf-Ti) and Q=r(m1-m2) to determine that 589 g of ice remain at 0 degrees Celsius after the water is brought to 0 degrees Celsius. This is because the heat exchange between the water and ice is enough to melt all the ice, which has a latent heat of fusion of 79.7 cal/g.

Homework Statement

It's a direct translation from italian, forgive the mistakes:

A container with thermically insulating walls has 2 parts, part A which contains a quantity m(A)=1230 g of water at a temperature of 15.6 degrees Celsius, and part B which contains a quantity m(B)=830 g of ice at a temperature of zero degrees Celsius. The two parts are divided by an insulating plate.

If the insulating plate is removed, what is the final temperature of the system?

What is the heat exchanged between water and ice?

(latent heat of fusion for ice: r=79.7 cal/g, specific heat of water: 1cal/gK, temperature of fusion of ice: 0degrees celsius)

Q=mc(Tf-Ti)
Q=r(m1-m2)

The Attempt at a Solution

It's just an attempt :)

Q to bring water to zero degrees = 1230 * 1 * (0-15.6) = -19188

19188 = r *(m1-m2)
19188= 79.7*(830-x)
19188 = 66151 - 79.7x
x= 589 g

So 589 g of ice are still there at the temperature of equilibrium, which then is 0 degrees Celsius.

It should be correct, but I do not understand why I should bring the water to 0 degrees. Though, it's the only way I manage to do it.

I tried to solve it considering the final temperature as an unknown quantity, but then the unknown quantities were two, with only one equation.

Please give me a method to understand what the final temperature is without me guessing it at first.

Thanks!

I hate late night thoughts as too many lately have been way off, but before a phase change, all of the water gets to zero C, if possible. I'll tell you why I suspect so--my friend brought over these odd plastic beverage containers that contain some water or fluid in the hollow beverage container itsself. I poured some soda into one, and after three hours it was shockingly cold. Short of slosh I have never had a beverage that cold.

fluvly said:
If the insulating plate is removed, what is the final temperature of the system?

What is the heat exchanged between water and ice?

(latent heat of fusion for ice: r=79.7 cal/g, specific heat of water: 1cal/gK, temperature of fusion of ice: 0degrees celsius)

...

The Attempt at a Solution

It's just an attempt :)

Q to bring water to zero degrees = 1230 * 1 * (0-15.6) = -19188

19188 = r *(m1-m2)
19188= 79.7*(830-x)
19188 = 66151 - 79.7x
x= 589 g

So 589 g of ice are still there at the temperature of equilibrium, which then is 0 degrees Celsius.

It should be correct, but I do not understand why I should bring the water to 0 degrees. Though, it's the only way I manage to do it.
Your method is correct. The reason you bring it to 0 is evident in your answer. Is there enough heat transferred from the water to melt all the ice? What is the temperature of ice?

AM

What is thermodynamics?

Thermodynamics is the branch of science that studies the relationships between heat, energy, and work.

How does thermodynamics relate to everyday life?

Thermodynamics plays a crucial role in our everyday lives, from the functioning of our bodies to the operation of machines and appliances. It helps us understand the transfer of energy and the efficiency of processes.

What are the laws of thermodynamics?

The laws of thermodynamics are fundamental principles that govern energy transfer and transformation. The first law states that energy cannot be created or destroyed, only transformed. The second law states that the total entropy (disorder) of a closed system always increases. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

What is the difference between heat and temperature in thermodynamics?

Heat and temperature are often used interchangeably, but in thermodynamics, they have distinct meanings. Heat is the transfer of energy from a hotter object to a colder object, while temperature is a measure of the average kinetic energy of particles in a substance.

How is thermodynamics used in engineering?

Thermodynamics is essential in engineering, as it helps in designing and optimizing systems and processes that involve energy transfer. It is used in fields such as power generation, refrigeration, and propulsion systems.