# Calorimetry Problem: Solving for Final Equilibrium Temp.

• a077456
In summary, the final equilibrium temperature of the system is 100 degrees Celsius. The specific heats of aluminum, water, and steam were given, and using the equation Qloss = Qgain, the final temperature was calculated to be 100 degrees Celsius. However, the calculation must also consider the latent heat of fusion from steam to water, which explains why the temperature remains at 100 degrees Celsius during the phase change. Taking this into account, the final equilibrium temperature of the system is 100 degrees Celsius.
a077456

## Homework Statement

A 300-g aluminum vessel contains 200 g of water at 10 0C.
100 g of steam at 1000C is poured into the container, what is the final equilibrium temperature of the system?

## Homework Equations

Given that the:
specific heat of Al = 910 J/kg 0C.
specific heat of water = 4190 J/kg 0C.
specific heat of steam = 2108 J / kg0C.

## The Attempt at a Solution

I am using the $$\left|$$Qloss| = $$\left|$$Qgained|
$$\left|$$( mc$$\Delta$$T ) steam = $$\left|$$( mc$$\Delta$$T ) Al + $$\left|$$( mc$$\Delta$$T ) water |

(0.1kg) ( 2108) (1000C - Teq) = [(0.3kg) (910) (Teq - (100C )) ]+ [(0.2kg) (4190) ((Teq - 100C) ]

after solving the equation, I have got Teq = 24.28 0C
However, according to the solution, the answer should be Teq = 100 0C. [\b]

I am just wondering how should the setup be? Do I have to consider that the steam is actually turning into ice or ice turning into steam? Therefore, should we also use the Q = mL where L is the latent heat; m = mass and Q = heat?

THank you very much and I am looking forward to hear any reply!

Last edited:
Your'e forgetting about the latent heat of fusion from steam to water but still I wouldn't have thought it would equalize at 100 degrees. And what ice are you talking about?

I think I made a mistake in that part. I was trying to say that the steam turn into water. So which would be the case: 1) all water 2) Water + Steam left over in the final stage?

I have tried to encounter with the Latent heat part, and it will be as follow:

Let L of steam = 2108

| (mc (delta T) + mL) of steam | = | mc (delta T) of Al + mc (delta T) of water |
(0.1kg) ( 2108) (100 C - 100 C) + m (2108) = [(0.3kg) (910) (Teq - (100C )) ]+ [(0.2kg) (4190) ((Teq - 100C) ]

Then at this point, I would have 2 unknowns, which is the mass of steam condensed, and the Teq, which is what I am looking for...

How should I approach this problem? Thank you very much !

I have understand how to do this problem now. Thanks!
This is because at the phase changes stage, steam is converting into water, therefore the temperature must stay at 100 degree.

Hello,

Thank you for your question. Your attempt at solving the problem using the equation \left|Qloss| = \left|Qgained| is correct. However, there are a few things that need to be considered in this problem.

Firstly, it is important to note that the system is in a closed container, meaning that there is no heat exchange with the surroundings. This means that the total energy of the system remains constant, and thus, the total heat lost by the steam must be equal to the total heat gained by the aluminum and water.

Secondly, it is important to consider the phase changes that may occur in the system. In this case, the steam will condense into water when it comes into contact with the cooler aluminum and water. This means that the latent heat of vaporization of the steam (Q = mL) must also be taken into account in the equation.

Taking these factors into consideration, the correct setup for the equation would be:

\left|Qloss| = \left|Qgained|

\left|( mc\DeltaT ) steam + Qvap | = \left|( mc\DeltaT ) Al + \left|( mc\DeltaT ) water |

Where Qvap is the latent heat of vaporization for steam (mL).

Solving this equation will give you the correct final equilibrium temperature of the system.

I hope this helps clarify the setup for the problem. Keep up the good work with your scientific problem-solving skills!

Best,

## 1. What is calorimetry and how is it used to solve for final equilibrium temperature?

Calorimetry is the scientific measurement of heat transfer in a system. It is used to determine the final equilibrium temperature of a system by measuring the heat gained or lost by the system and its surroundings.

## 2. What is the equation used to solve for final equilibrium temperature in a calorimetry problem?

The equation used is Q = mCΔT, where Q is the heat transferred, m is the mass of the system, C is the specific heat capacity, and ΔT is the change in temperature.

## 3. How do you determine the specific heat capacity of a substance in a calorimetry problem?

The specific heat capacity of a substance can be determined experimentally by measuring the heat transferred and the change in temperature of the substance, and then using the equation C = Q/mΔT.

## 4. What are the assumptions made in a calorimetry problem?

The assumptions made in a calorimetry problem include: no heat is lost to the surroundings, no phase changes occur, and the specific heat capacity of the system remains constant throughout the experiment.

## 5. Can calorimetry be used to solve for the final equilibrium temperature in any type of system?

Yes, calorimetry can be used to solve for final equilibrium temperature in any type of closed system, as long as the assumptions mentioned above are met.

• Introductory Physics Homework Help
Replies
7
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
5K
• Introductory Physics Homework Help
Replies
14
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
5K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
6K
• Introductory Physics Homework Help
Replies
7
Views
9K