Exploring Heat Energy in Potato Chips

So if we want to find out how many calories of heat energy are in this potato chip, we can set it on fire. This is going to cause it to release heat energy to the water that's in the container above it. The water is going to absorb this heat energy and its temperature is going to rise as a result. So if we find out how much the temperature of the water rose, we can calculate how much heat energy it absorbed. This is important because it should be the same amount. that the potato chip released. And that should be the same amount that the potato chip had in it to start with before it started releasing it to the water. So to calculate how much heat energy the water absorbed, we're going to use this equation, Q equals m times C times delta T. So if we're going to do some math, we need some numbers. If you've done this experiment yourself in lab, you should have your own numbers, data that you recorded during the experiment. But for these problems here, We'll use some numbers that I came up with. So, let's say that in our container we have 150 milliliters of water. Now remember, one milliliter of water has a mass of one gram. which means that 150 milliliters of water have a mass of 150 grams. We'll also need to know the temperature change for the water. So the initial temperature before we started burning the potato chip under the water is 21 degrees Celsius. And then after the potato chip is finished burning, the final temperature is 85 degrees. Okay? So now we can start working with some variables in this equation. Let's talk about what they are. So Q is going to be the heat absorbed by the water. This is the variable that we're going to be solving for. M is the mass of the water. We know that it's right up here 150 grams. Remember it's 150 grams because one milliliter of water has a mass of one gram. So 150 milliliters has a mass of 150 grams. Now C the specific heat of the water. So specific heat is how many calories. Calories are required to take one gram of water and raise its temperature by one degree Celsius. You might remember that for water, this is one calorie is required to raise one gram of water by one degree Celsius. So that's what all these units are. If you didn't remember this, you could easily find the number for water-specific heat on the internet or in a book. Okay. Now, finally, delta T. the change in temperature of the water. So to find delta T, we're going to do the final temperature minus the initial temperature. So we're going to do 85 degrees Celsius minus 21 degrees Celsius, and that's going to give us 64 degrees Celsius for our delta T. Now we have m and c and delta T, so we can plug these into the equation. We'll do q, and we equals m 150 grams times c one calorie over grams times degrees celsius times delta t which is 64 degrees celsius. I'm just going to clean some stuff up here so we can have this at the top. So here's our equation. To find q all we have to do is multiply through this. It's going to be 150 times 1 times 64 and that is going to give us 9,600. What are the units going to be? Let's look at what cancels out. We have grams up here, grams down there, so they cancel. Degrees Celsius here, degrees Celsius up there, leaving us with calories. This is going to be 9,600 calories. Now, we're not quite done though because we don't have the right units. These calories here, the answer to this question, these are different kinds of calories. than the calories in food. In fact, there are a thousand of these kind of calories in one food calorie. Okay, a thousand calories of these in one food calorie. We can also call a food calorie a kilocalorie. And that kind of makes sense because kilo means a thousand. So we have a thousand of these in one of these. Now, just to make things super confusing, if you spell the word calorie with an uppercase C, you're talking about a thousand calories. talking about kilocalories or food calories, which means that a calorie with an uppercase C has a thousand lowercase c calories in it. So anyway, we're going to have to be converting from these kind of calories into this food calorie. I usually just call this a kilocalorie. So it's not too confusing with upper or lowercase c. Now, we can take this relationship, 1,000 little c calories to 1 kilocalorie, and use that to write two conversion factors, 1 kilocalorie over 1,000 calories, or we can just flip it. So, which of these are we going to want to use? We're starting with 9600 little c calories and we're going to want to use the conversion factor that is going to get rid of calories. So calories is on the top here, we want to use a conversion factor that's going to have calories on the bottom so we're going to use this one. Now we multiply them together. And we'll do 9,000 times 1 divided by 1,000. Calories on top, calories on the bottom. They cancel out and we're going to end up with 9.6 kilocalories. Also known as food calories or capital C calories. So 9.6 kilocalories of heat energy are in that potato chip. Now this might be... all the math that you need to do to find out that 9.6 food calories are in that potato chip. But just in case, we're going to go through and do a little bit more math. First we're going to find out how many calories per gram are in the potato chip. Then we're going to calculate how many calories per serving. And then we're going to compare our answer to the answer on the back of the potato chip package. And we're going to use percent error to figure out how close we were or how far off we were. So we found out that there are 9.6. 9.6 food calories, also known as kilocalories, in that potato chip. Now, you might be asked to convert this number into joules. I'm not going to show how to do that here because there are many videos you can find for how to convert between calories and joules. The first thing we're going to do here is we are going to calculate how many calories per gram are in this potato chip. So, we know how many calories in the potato chip, 9.6. We will need to find out the mass of the potato chip. Let's say that I... I weighed it ahead of time and found out that its mass is 1.75 grams. So now all we're going to do is 9.6 calories divided by its mass, 1.75 grams. I'm going to do this math and round it to significant figures and I'm going to get 5.5 calories per gram. Now, I can take this information, calories per gram, and move this up here, and I can use this to calculate the calories per serving. In order to do this, I'm going to have to look at the back of the potato chip. package to the nutrition facts and it's going to tell me what the serving size is right this is like the amount that you're supposed to eat in one serving so here for this potato chip a package it says that the serving size is 34 grams so how many calories are in in one serving. We know how many calories are in one gram and we know how many grams are in one serving so this shouldn't be too difficult. What we're going to do is we're going to take our serving size of 34 grams and multiply it by our calories per gram so 5.5 calories per gram. The grams are going to cancel out. So we're going to add in the I'm going to go through and do the math, 34 times 5.5, and that's going to give me 190 calories in one serving. So we got 190 calories. If we look on the back of the package, it says that amount of calories per serving is actually 210. So we were a little bit off. So let's calculate percent error to find out how off we were. To do this, we're going to take the actual value and subtract the measured value and divide all of that by the actual value. So here's what we're going to do. Going to take the actual value which is a number that's actually on the back of the package. That's going to be 210, I'm not going to use units here just because it's a pain, 210 minus the measured value 190. I'm going to take the absolute value of that and divide it again by the actual value which is 210. And I'm then going to multiply that by 100%. So when I do this out, I get a percent error of 11%. And that tells us how far off we were. Now here's a question. Why were we off? Why was this number smaller than it should have been if we'd done the experiment perfectly? Well, here's a reason why. Remember that we're assuming... that all of the energy that that burning potato chip releases goes into the water. So that if we measure the amount of heat energy that the water has absorbed, we're also measuring all the amount of heat energy that the potato chip released. But that's not true. And here's why. Here's our potato chip burning. The heat energy represented by these arrows doesn't just go into the water, right? It's also warming the air around it. So not all the heat gets... absorbed by the water. Only some of it does. So that's why the number that we got from the experiment was smaller and a little bit off from the actual number of calories that are in that potato chip.

So if we find out how much the temperature of the water rose, we can calculate how much heat energy it absorbed. This is important because it should be the same amount. that the potato chip released. And that should be the same amount that the potato chip had in it to start with before it started releasing it to the water. So to calculate how much heat energy the water absorbed, we're going to use this equation, Q equals m times C times delta T.

So if we're going to do some math, we need some numbers. If you've done this experiment yourself in lab, you should have your own numbers, data that you recorded during the experiment. But for these problems here, We'll use some numbers that I came up with. So, let's say that in our container we have 150 milliliters of water. Now remember, one milliliter of water has a mass of one gram.

which means that 150 milliliters of water have a mass of 150 grams. We'll also need to know the temperature change for the water. So the initial temperature before we started burning the potato chip under the water is 21 degrees Celsius.

And then after the potato chip is finished burning, the final temperature is 85 degrees. Okay? So now we can start working with some variables in this equation.

Let's talk about what they are. So Q is going to be the heat absorbed by the water. This is the variable that we're going to be solving for.

M is the mass of the water. We know that it's right up here 150 grams. Remember it's 150 grams because one milliliter of water has a mass of one gram. So 150 milliliters has a mass of 150 grams.

Now C the specific heat of the water. So specific heat is how many calories. Calories are required to take one gram of water and raise its temperature by one degree Celsius. You might remember that for water, this is one calorie is required to raise one gram of water by one degree Celsius.

So that's what all these units are. If you didn't remember this, you could easily find the number for water-specific heat on the internet or in a book. Okay.

Now, finally, delta T. the change in temperature of the water. So to find delta T, we're going to do the final temperature minus the initial temperature. So we're going to do 85 degrees Celsius minus 21 degrees Celsius, and that's going to give us 64 degrees Celsius for our delta T. Now we have m and c and delta T, so we can plug these into the equation.

We'll do q, and we equals m 150 grams times c one calorie over grams times degrees celsius times delta t which is 64 degrees celsius. I'm just going to clean some stuff up here so we can have this at the top. So here's our equation. To find q all we have to do is multiply through this. It's going to be 150 times 1 times 64 and that is going to give us 9,600.

What are the units going to be? Let's look at what cancels out. We have grams up here, grams down there, so they cancel.

Degrees Celsius here, degrees Celsius up there, leaving us with calories. This is going to be 9,600 calories. Now, we're not quite done though because we don't have the right units. These calories here, the answer to this question, these are different kinds of calories. than the calories in food.

In fact, there are a thousand of these kind of calories in one food calorie. Okay, a thousand calories of these in one food calorie. We can also call a food calorie a kilocalorie.

And that kind of makes sense because kilo means a thousand. So we have a thousand of these in one of these. Now, just to make things super confusing, if you spell the word calorie with an uppercase C, you're talking about a thousand calories. talking about kilocalories or food calories, which means that a calorie with an uppercase C has a thousand lowercase c calories in it. So anyway, we're going to have to be converting from these kind of calories into this food calorie.

I usually just call this a kilocalorie. So it's not too confusing with upper or lowercase c. Now, we can take this relationship, 1,000 little c calories to 1 kilocalorie, and use that to write two conversion factors, 1 kilocalorie over 1,000 calories, or we can just flip it.

So, which of these are we going to want to use? We're starting with 9600 little c calories and we're going to want to use the conversion factor that is going to get rid of calories. So calories is on the top here, we want to use a conversion factor that's going to have calories on the bottom so we're going to use this one. Now we multiply them together. And we'll do 9,000 times 1 divided by 1,000.

Calories on top, calories on the bottom. They cancel out and we're going to end up with 9.6 kilocalories. Also known as food calories or capital C calories. So 9.6 kilocalories of heat energy are in that potato chip. Now this might be...

all the math that you need to do to find out that 9.6 food calories are in that potato chip. But just in case, we're going to go through and do a little bit more math. First we're going to find out how many calories per gram are in the potato chip.

Then we're going to calculate how many calories per serving. And then we're going to compare our answer to the answer on the back of the potato chip package. And we're going to use percent error to figure out how close we were or how far off we were.

So we found out that there are 9.6. 9.6 food calories, also known as kilocalories, in that potato chip. Now, you might be asked to convert this number into joules.

I'm not going to show how to do that here because there are many videos you can find for how to convert between calories and joules. The first thing we're going to do here is we are going to calculate how many calories per gram are in this potato chip. So, we know how many calories in the potato chip, 9.6.

We will need to find out the mass of the potato chip. Let's say that I... I weighed it ahead of time and found out that its mass is 1.75 grams. So now all we're going to do is 9.6 calories divided by its mass, 1.75 grams.

I'm going to do this math and round it to significant figures and I'm going to get 5.5 calories per gram. Now, I can take this information, calories per gram, and move this up here, and I can use this to calculate the calories per serving. In order to do this, I'm going to have to look at the back of the potato chip.

package to the nutrition facts and it's going to tell me what the serving size is right this is like the amount that you're supposed to eat in one serving so here for this potato chip a package it says that the serving size is 34 grams so how many calories are in in one serving. We know how many calories are in one gram and we know how many grams are in one serving so this shouldn't be too difficult. What we're going to do is we're going to take our serving size of 34 grams and multiply it by our calories per gram so 5.5 calories per gram.

The grams are going to cancel out. So we're going to add in the I'm going to go through and do the math, 34 times 5.5, and that's going to give me 190 calories in one serving. So we got 190 calories. If we look on the back of the package, it says that amount of calories per serving is actually 210. So we were a little bit off. So let's calculate percent error to find out how off we were.

To do this, we're going to take the actual value and subtract the measured value and divide all of that by the actual value. So here's what we're going to do. Going to take the actual value which is a number that's actually on the back of the package.

That's going to be 210, I'm not going to use units here just because it's a pain, 210 minus the measured value 190. I'm going to take the absolute value of that and divide it again by the actual value which is 210. And I'm then going to multiply that by 100%. So when I do this out, I get a percent error of 11%. And that tells us how far off we were. Now here's a question.

Why were we off? Why was this number smaller than it should have been if we'd done the experiment perfectly? Well, here's a reason why.

Remember that we're assuming... that all of the energy that that burning potato chip releases goes into the water. So that if we measure the amount of heat energy that the water has absorbed, we're also measuring all the amount of heat energy that the potato chip released.

But that's not true. And here's why. Here's our potato chip burning.

The heat energy represented by these arrows doesn't just go into the water, right? It's also warming the air around it. So not all the heat gets... absorbed by the water.

Only some of it does. So that's why the number that we got from the experiment was smaller and a little bit off from the actual number of calories that are in that potato chip.

Transcript for:Exploring Heat Energy in Potato Chips

Transcript for:
Exploring Heat Energy in Potato Chips