Advanced Calorimetry: Equilibrium Temperature with Phase Changes: Study with Video Lessons, Practice Problems & Examples

In calorimetry problems involving temperature and phase changes, determining the final equilibrium temperature can be complex. Begin by analyzing the heat transfer between substances, such as copper and water, considering their specific heat capacities. Use the equation for heat transfer, QA = mc, and account for phase changes using latent heat. If the calculated temperature exceeds boiling, adjust calculations to include vaporization, ensuring accurate results for equilibrium temperature and phase transitions.

Calculating Equilibrium Temperature in Calorimetry Problems with Phase Changes

Hey, guys. So up until now when we've seen calorimetry problems that included both temperature and phase changes, we were told what the equilibrium temperature was going to be. But in some cases, you're actually going to have to calculate that. You're going to have to calculate what that final equilibrium temperature is. Unfortunately, that makes these problems a little bit harder. These problems are kind of rare, but they are trickier. So in this video, I'm going to show you a different sequence of steps than the ones that we've seen so far to solve these kinds of problems. Let's go ahead and check out our example here. We've got these two substances. We've got copper at 150 degrees Celsius and we've got mixing with water at 30 degrees Celsius. So we're going to close them, mix them in a container, and we want to calculate what the final temperature of this mixture is. So remember, before we actually write out our calorimetry equations, the first thing we want to do is draw our diagrams and indicate what the initial and final temperatures are. That's the sort of 0th step. So I've got these two different substances, copper and water. Copper is always a solid up until 1,000 degrees Celsius. This one's going to start here at 150 degrees. That's our hotter one. It doesn't have to do this scale, it doesn't matter. Right? The water on the other hand is going to be at 30 degrees Celsius, and we've got, you know, our sort of familiar diagram here. So here's what's going on. The copper is going to lose some heat and therefore lose some temperature. It's only going to go down in temperature, it can't experience a phase change. But the water on the other hand can actually do a couple of different things. So what we have to do is indicate where the initial or the final temperature is, but we actually don't know where that is. So the problem with this is that there are three possibilities here. The water could absorb enough heat from the copper so that it goes up in temperature only. So imagine this basically just goes higher here on this diagram and we only experience a temperature change. There could be even more heat though from the copper such that the water actually starts to boil, so it starts to transition into steam. And then if there's enough heat, there's enough heat to actually turn this thing completely into steam that the temperature actually could continue rising. The problem is we actually don't know upfront which one of these possibilities could actually be true. So what happens here is we have three possibilities. Right? So we have water, damn water, the specific heat for water, turning all the way to a 100 degrees. Then we've got some of that water which could melt or, sorry, boil into steam, and then we've got some of this steam that can actually increase in temperature as well. So these are the three different terms that we could possibly have inside of our calorimetry equation. On the right side, we're only going to have the copper. Right? So mc _c Δt _copper for copper. So the problem we're basically going to do here before I get into the sort of messy steps is in order to figure out how many of these terms actually exist inside of our equations, gonna have to do a little bit of trial and error. Basically, in these problems, you're going to have to figure out the number of MCAT or ML equations inside of your calorimetry equations. And we do that by calculating some stuff, by making some assumptions. We're going to try some things, and if it doesn't work, we're going to have to go back here and change some things and then just try again. It's a lot of trial and error. Alright. So let's go ahead and get to the steps

Here’s what students ask on this topic:

How do you calculate the final equilibrium temperature in calorimetry problems involving phase changes?

To calculate the final equilibrium temperature in calorimetry problems involving phase changes, follow these steps:

1. Identify the substances involved and their initial temperatures.

2. Determine the specific heat capacities and latent heats for phase changes.

3. Assume no phase change initially and use the heat transfer equation:

$Q=mc\Delta T$

4. If the calculated temperature exceeds a phase change point, adjust calculations to include latent heat:

$Q=mc\Delta T+mL$

5. Iterate until the correct equilibrium temperature is found.

What are the common mistakes to avoid when solving calorimetry problems with phase changes?

Common mistakes to avoid include:

1. Ignoring phase changes: Always check if the temperature crosses a phase change point.

2. Incorrectly applying specific heat capacities: Use the correct specific heat for each phase.

3. Neglecting latent heat: Include latent heat for phase transitions (e.g., melting, boiling).

4. Sign errors: Ensure correct signs for heat gained or lost.

5. Incorrect mass assumptions: Verify the mass of the substance undergoing phase change.

6. Not iterating: Recalculate if initial assumptions are incorrect.

Why is trial and error often necessary in calorimetry problems with phase changes?

Trial and error is necessary because the final equilibrium temperature depends on whether phase changes occur. Initial assumptions may be incorrect, requiring recalculations. For example, assuming no phase change might yield a temperature above the boiling point, indicating a phase change must be included. Iterating with different assumptions ensures accurate results, accounting for all possible heat transfers and phase transitions.

How do you account for latent heat in calorimetry calculations?

To account for latent heat in calorimetry calculations, include the energy required for phase changes. Use the equation:

$Q=mc\Delta T+mL$

where $m$ is the mass, $c$ is the specific heat, $\Delta T$ is the temperature change, and $L$ is the latent heat. This ensures the energy for phase transitions (e.g., melting, boiling) is included in the total heat transfer.

What is the significance of specific heat capacity in calorimetry problems?

Specific heat capacity is crucial in calorimetry problems as it determines the amount of heat required to change the temperature of a substance. It is defined as the heat needed to raise the temperature of 1 kg of a substance by 1°C. The equation:

$Q=mc\Delta T$

uses specific heat capacity ($c$) to calculate heat transfer. Different substances have different specific heat capacities, affecting how they absorb or release heat, which is essential for accurate calorimetry calculations.