Heat Capacity (for people who prefer formulas and algebra)

Heat capacity problems are always interesting because they are one of the types of science problems that you can often work through with just a little bit of insight into what heat capacity is, even if you don't know the "correct" way to do the problem. Heat capacity is the energy required to change the temperature of a substance. If you can keep track of energy, amount of the substance, and the temperatures before and after the change, you just might be able to cobble together the quantities and arrive at the right answer.

But I know, sometimes you just want to memorize a mathematical formula and plug numbers in. If that's what you're looking for, then this is just for you. Heat capacity problems can pretty much all be solved using the formula:

(Energy transferred) = (Heat capacity) x (Amount of substance) x [(Final temperature) - (Initial temperature)]

Or, if we want to make that shorter:

E = (C_p) x (g) x (T_final - T_initial)

Let's plug in information from 2 different problems:

1. A 250.0g sample of water (C_p = 1 ^calorie/_(g)(°C)) is heated from 14.3°C to 27.4°C. How many calories of heat energy have been transferred?
Plugging in to the formula:

E = (1 ^calorie/_(g)(°C)) (250.0g) (27.4°C - 14.3°C) = 3275calories

2. A 400.0g sample of water is initially at 16.8°C. If 5000 calories of energy is added to the water, what is the final temperature?
Plugging in again:

5000 calories = (1 ^calorie/_(g)(°C)) (400.0g) (T_final - 16.8°C)

Same thing, but now we have to do a little algebra to solve for T_final, and we get a final temperature of 29.3°C.

If you prefer a more descriptive solution to heat capacity problems, take a look at http://scienceofcooking100.blogspot.com/2015/11/heat-capacity.html

Heat Capacity

There have been a few questions about heat capacity…

Heat capacity is a measure of the amount of heat required to change the temperature of a given amount of a substance by some amount. A common unit for heat capacity is "calories / (gram)(°C)". For water, heat capacity is 1 calorie / (gram)(°C), so if I have 1 gram of water and I want to increase its temperature by 1°C, I have to add 1 calorie of energy to the water. What if I have more than 1 gram or I want to increase the temperature by more than 1°C? Multiply!

The reverse of this problem is really the same problem, it just requires some different math. What if I have 18.00mL of water that is initially at 12.6°C and I add 49calories of energy to that water? First part… the density of pure water is 1 g/mL so 18.00mL of water has a mass of 18.00g. Now, if the heat capacity of water is 1 calorie / (gram)(°C), and we have 18.00g of water, we can again multiply to get:

{1 calorie / (gram)(°C)} x 18.00g = 18.00 calories per °C

So for every 18.00 calories of energy we add to this specific sample, we will increase the temperature by 1°C. We are adding 49 calories to this specific sample so:

49 calories / 18.00 calories per °C = 2.7°C

This is how much the temperature changes when we add this amount of energy. Since the sample was initially at 12.6°C and we added energy, the new final temperature must be 2.7°C higher than the initial temperature, 12.6°C + 2.7°C = 15.3°C.

There are some assumptions in this description (like the density of water) that simplify the problem… if you want to get the absolutely perfectly correct answer, you'd have to take some of those assumption into account, but this is close enough for our purposes.

Microwave Heating Experiment (Fall 2015)

There are quite a few questions about the Microwave Heating experiment (procedure here), so let me try to address them all in one place.

The most common and persistent questions are related to the data analysis. The hands-on procedure and collection of the data seems to be going well, so let's not dwell on that part of the experiment. Once you have collected your data, you'll have a sea of numbers that you, as a scientific investigator, will have to process and interpret so you can get some useful information out of your experiment. The data you are collecting will look something like this:

The procedure tells you to prepare a graph of this data. Whenever you are collecting data (or just observing something interesting in your daily life) where one variable is under your control (in the case of this specific example, time), and another variable is simply a quantity you are measuring (in this case, temperature), it is ALWAYS interesting to consider what the graph of that information looks like. In this case, the graph of the above data looks like:

Hmm, interesting, although in this case not too surprising: as more time in the microwave passes, the sample gets hotter. But how much hotter? And how fast does it get hotter? If I want to heat a cup of water to make tea, should I put it in the microwave for 30 seconds or 5 minutes? The rate of heating is an interesting and important piece of information we can extract from this data!

How do we calculate a rate? Rate is the change in some observable quantity divided by the change in time. If you can eat a cheeseburger in 5 minutes, your rate of eating cheeseburgers is:

Change in the number of cheeseburgers / Change in time

1 cheeseburger / 5 minutes = 0.2 cheeseburgers per minute

In this experiment, you weren't eating cheeseburgers (well, OK, I guess you might have been eating cheeseburgers while you were watching water heat up…), but you were observing the change in temperature as time passed, so we should be able to calculate a rate in a similar way. Looking back at the data above, we can pick any two points and look at the change in temperature divided by the change in time. For example, from 90 seconds to 135 seconds the temperature changed from 116.04°C to 184.70°C, so the rate over that time period was:

(184.70°C - 116.04°C) / (135 seconds - 90 seconds)

(68.66°C) / (45 seconds)

1.5°C per second

We could pick any two points out of our data and calculate a rate, and they would all be pretty similar, but because there is some variability in our experiment they would not all be identical. But wait, if that's all we are going to do, then why did we make a graph? Graphs are pretty, but making a graph for the sake of making a graph doesn't seem like a great use of your time. Can we use the graph to determine the rate of heating? Hmm, change in temperature… the vertical axis (y-axis) is temperature, so that one should track changes in temperature… and the horizontal axis (x-axis) is time… WAIT! The data points in the graph look pretty close to linear, and the slope of a line is "rise over run"… if "rise" is the change in the y-axis variable and "run" is the change in the x-axis variable, then we should be able to get the slope from the graph, and the slope should be the rate of heating! If we draw a line that looks like it fits the data pretty well, we get:

From the line (we're not looking at specific points now), it looks like over the time period from 0 seconds to 300 seconds the temperature rises from about 5°C to about 390°C. So the rate based on the fit line is:

(390°C) / (300 seconds)

1.3°C per second

By using a fit line, we can even out some of the variability associated with any two points we might choose and we should get a more reliable answer. If we look at the rate for any two adjacent points (any 15 second period in our experiment) and calculate the rate using only those two points, we would get answers as low as 0.75°C per second and as high as 1.9°C per second, so using the fit line seems like a pretty good way to get a reliable single answer for the experiment.

Good luck on your data collection and analysis.

Fall 2015 - Welcome to class!

Fall 2015 semester has begun! Welcome to BCBT 100 - The Science of Cooking. Together we will explore the scientific foundations that humans (and pre-humans...) have used for millenia to produce and transform food. If you have ever prepared or even just eaten food, you are a scientist!

Let's have a great semester!

Make a graph

Help me help you. There seems to be some confusion that I'd really like to be able to clear up and I'd welcome some feedback. In the at-home lab activity we recently did for class (http://www.drbodwin.com/teaching/scicook/MicrowaveHeating20140227a.docx), the first data analysis section says:

My intention here was that the students would take the time-dependent temperature data they collected and prepare a plot that looks something like this:

{NOTE: This plot contains more data that I expect in the student experiment.}

A significant number of students did not realize that they needed to include a graph as part of their data analysis and assignment. I don't understand why this was not clear. I am not being snarky or condescending or angry or mean when I say that, I honestly don't understand why that instruction in the "Data Analysis" isn't clear, so I would sincerely appreciate any help on how to write that instruction more clearly. I have a couple ideas of why this was not an effective instruction:

1. The word "plot" doesn't mean the same thing to everyone. Is there a better word that would make this more clear? Graph? "X-Y scatter plot"? I do not require students to use a spreadsheet to generate their plots because I don't want to introduce additional barriers and hand-drawn plots/graphs are sufficient for the data presentation and analysis in this class… Would it be better to require computer generated plots/graphs just to reinforce that a graph is required for the data presentation and analysis?
2. Is this more a symptom of the broader problem of "science is hard" rather than poorly written instructions? If a student firmly believes that "science is hard" or "I'm not good at math", then the student is likely to accept a lower standard for himself or herself and perform below his or her abilities. 
3. Do the students just not care? I refuse to believe that this is the most common problem; the vast majority of the students in this class are dedicated hard workers and really want to learn something. At the same time, the students taking this class are not (on average) the typical "sciencey" student, they are taking this course because they see it as one of the easier options for fulfilling the science requirement of their degree. That means that there are at least a few (and they're usually not that hard to identify) who are just in the class to do the bare minimum to pass and have no real interest in learning any more than they need to squeak by with a "C".

There is no magic single answer to this issue, BUT if there are some simple fixes (change the wording, etc) that will help some students succeed in this class, I'm happy to consider them. Anonymous comments are permitted here, so feel free to be as open as you would like. I'm always open to learning new and better ways to do things, so open feedback is helpful.

Lab Assignment Tips

After looking over your Lab 1 assignments, there are a couple general points that I think would help everyone make some improvements on future assignments:

1. Individual vs Group Assignments

For your labs (and everything else in BCBT 100), you must turn in individual assignments to receive a grade. Even if you're working with a partner (or 2) on a lab experiment, each partner is required to turn in an individual assignment for grading. This doesn't just mean 2 copies of the same assignment with a different name at the top (that would be plagiarism and could result in your expulsion from the University), but individual assignments from each partner. I expect and encourage you to discuss your experimental observations and conclusions with others in the class, and if you are working with a partner I expect that the raw data you use will be the same, but your responses to questions should be yours and in your voice. 

2. Complete Answers
Especially in labs, always assume that there is a "Why?" or an "Explain" part of every question. Give me an answer that shows me a little bit of your thought process. "How confident are you in the accuracy of your result?" shouldn't just be answered with "Very confident" or "Yes." {I'm not sure how "Yes" even could be an answer to that question...} If you are "very confident" in your result, there must be some reason for your confidence. And no, the answer is not "I am very confident in my result because I am just that good." An answer that would be quite convincing and give me a good indication of your thought process would be something like "The error in our repeated measurements {+/- 0.014} is quite small compared to the average of the repeated measurements {17.372}, so we are very confident in the precision of our answer." I can say with nearly 100% certainty that I will almost never ask a question that I expect to be answered with a single word. 

3. Show Your Work

Whenever you have to do any math, show at least 1 sample calculation for each step of the math you have to do. It's not always obvious there some of your numbers come from, so a little bit of help would be nice. {This is closely related to the "Complete Answers" tip above...}

4. Graphs Should Fill the Available Space

This is especially true when you're trying to fit a line to a bunch of data points by eye. If you have a half page of space for your graph, don't squeeze all the data into a little postage stamp in the corner. By spreading out the data, you will minimize the error in your line fit. Scientists devote a stunning amount of time to analyzing and trying to minimize error in their experiments; be a good scientist!

I'll post more tips as they come up. When in doubt, always ask.

Study Guide Answers

A few people have asked if I'm going to post "answers" to the study guide for Exam 2.

Short answer = no.

Less short answer = The "answers" are already posted. For Exam 1 I posted specific sample multiple choice questions, so there was an answer key. For Exam 2 (and likely Exams 3 & 4...), I posted a study guide that contains open-ended questions. The answers to these questions are contained in the slides I used in class and/or the assigned readings from the textbook. By posting questions this way, I hope to encourage you to think about many of these concepts a little more broadly rather than focus on picking the exact right answer from a list of possible choices.

For those of you who may be a little anxious that the exam will be a whole different format than Exam 1, fear not; your actual exam will still be multiple choice. By preparing for the exam with open-ended questions, you will be better prepared to answer a variety of multiple choice questions on each topic rather than just answer the exact questions you have studied. Some of the study guide questions will probably show up on the exam as multiple choice questions, but by preparing for those questions without the restriction of a specific set of multiple choice options, you will be better prepared to succeed.

If you really want to see something that looks like answers to some of the questions on the study guide, many of these can be found in one of these links:
http://www.drbodwin.com/teaching/scicook/bcbt100aexam2practicek.pdf
http://www.drbodwin.com/teaching/scicook/bcbt100aexam3practicek.pdf

Good luck.