Scienceblogs is promoting the writing of "Science 101" general topic posts all through the "back to school" month of September. So, here is the first in a multi-part series on Heat Capacity in Biology:
Heat Capacity in Biology 101: What is it?
Heat capacity is basically a proportionality constant. For any substance, the heat capacity tells you how much the temperature of the substance will change when you add a specific amount of heat.
Here is an absolutely beautiful schematic illustration of the difference between a small heat capacity and a large heat capacity (from a website on the physics of X-ray tube behavior) note the temperatures used in the illustration are a bit outside the temperature range that biologists are normally interested in, but the figure still illustrates the concept quite well).
When you apply heat to a substance with a low heat capacity, it will rise in temperature faster than a substance with a high heat capacity. (Keep reading, it gets to biology eventually...)
When you boil water, the temperature of the water stays at 100 degrees C regardless of how much heat you add, until it all boils away. The heat capacity of the water is approaching infinity at this point: it can absorb monstrous amounts of heat, but its temperature remains the same. This is typical behavior for substances during phase changes.
But before you hit the boiling point, the water will rise in temperature as you add heat. In fact, every milliliter (cubic centimeter) of water will rise 1 degree C for every calorie of heat you input - and this is in fact also the definition of a calorie.
"Heat capacity" is one thing, "heat capacity change" is a slightly different thing:
When substances change in any way (e.g. when they change phase, as in the boiling water example; or if they change via chemical reaction, etc.) their heat capacity will also frequently change - and then you get a "change in heat capacity" or ÎCp. (the "p" here denotes constant pressure - since biological reactions virtually all occur at standard, atmospheric pressure, the thermodynamic state functions used in biology are almost always the constant pressure forms rather than the constant volume forms).
Nomenclature alert: Although "heat capacity" and "heat capacity change" are truly different (one is a constant, the other is a difference between two constants) -- the two expressions are often used interchangeably in the literature -- in biology at least, if the sentence is talking about heat capacity, it almost always is actually talking about "heat capacity change".
So almost any reaction you might study in biology will exhibit a heat capacity change: protein folding, protein-protein interactions, protein-DNA binding, etc., all have measurable heat capacity changes (just like one can measure the heat capacity change between liquid water and gaseous water) - i.e., all of these processes and substances have one heat capacity (Cp) before the reaction and a different Cp after the reaction, and the difference between before and after = ÎCp.
Heat capacity and heat capacity changes are "thermodynamic state functions" - fundamental, equilibrium properties of a substance or a reaction system - just like free energy (ÎG), enthalpy (ÎH), and entropy (ÎS), among others.
Conclusion of Part 1: Wow, say you can (for example) measure the difference in heat capacity of proteins and DNA before and after they bind to one another (drum roll...) Who cares? (or as Dr. McCoy might say: "I'm a biologist Jim, why are you talking to me about frigging heat capacity?") Well, stay tuned for Part 2, coming up soon (very soon, because most of us who work on any aspect of heat capacity know that without connecting it to something biological or molecular, to many people it sounds like so much hot air).
Here is a link to a song called heat capacity, which appears to have nothing to do with heat capacity:
http://www.gametabs.net/dragon-ball-z-budokai-tenkaichi-3/heat-capacity
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Specific heat is a classical thermodynamic property of matter. It is not a stand alone "thing" that you analyze alone that tells you anything that way.
It is useful as a measure of thermal capacitance in a network where heat is moving around, and helps understand not only how much energy something absorbs, but is part of predicting static and dynamic energy equilibrium in a system that you isolate from the environment in order to understand what is happening thermodynamically inside the system.
Water is the most common high capacity element in many systems. You can taylor heat capacity by adding things to water, but it takes large amounts of "stuff" to change its heat capacity. (Changing other properties like freezing and boiling point is easier.)
The issue, as you stated is how you use it in a system. the problem is that typical heat transfer analysis methods, like forward differencing, break down in networks with very small isothermal nodes. Using it for analyzing proteins is not reasonable.
Semi-empiracle methods and relationship particular to nano sized elements have to be developed and correlated with measurements to be reliable. The payoff is that you can then start to understand the energy balance in very small networks, like cells. And that helps understand the chemistry and behavior of the network.
Heat capacity is most definitely not a state function. It's a path function. If you specify 'constant pressure' or 'constant volume' - i.e. specify a path -- then it becomes a state function.
In thermodynamics, precision in definitions is essential.
tank you
Conclusion of Part 1: Wow, say you can (for example) measure the difference in heat capacity of proteins and DNA before and after they bind to one another (drum roll...)
http://www.elemitasarim.com
I'm sorry, but heat capacity is neither state function (path independent) nor a path function, but a thermodynamic response function. In other words, it relates the fluctuations in the thermal energy of the system to the temperature, which is why it formally diverges on going through a first order phase transition (where those fluctuations become infinite). I definitely wouldn't describe it as just a constant of proportionality, even to a Biology 101 class, since as you said it isn't constant with temperature and it also contains important thermodynamic information about the system.
Although I'm not exactly sure what you'll be going on to say in Part 2, I presume it will something to do with the effect of protein binding on heat capacity, which is linked in a complicated way to the changes in conformation and vibrational modes in the substrate and solvent. Therefore, it is crucial to get across the idea that heat capacity is related to the number of accessible modes that the system has for absorbing thermal energy.
You guys realize that bickering over nomenclature (and I have rarely ever heard two thermodynamicists who did not bicker over nomenclature) is a major reason most people hate thermodynamics, right? And much of this bickering kind of ignores the main points of the post. E.g. Gerald seems to ignore that the heat capacity in the post is defined as constant pressure heat capacity, while lordaxil talks almost completely about statistical thermodynamics and not about the classical macroscopic thermo in the post, where heat capacity most definitely is both a state function and a proportionality constant, by definition on both counts. Your points are nice additions to this very introductory post, but they are not contradictions of it, and with a little less bickering to them they would be very interesting expansions of the topic.
'm sorry, but heat capacity is neither state function (path independent) nor a path function, but a thermodynamic response function. In other words, it relates the fluctuations in the thermal energy of the system to the temperature, which is why it formally diverges on going through a first order phase transition (where those fluctuations become infinite). I definitely wouldn't describe it as just a constant of proportionality, even to a Biology 101 class, since as you said it isn't constant with temperature and it also contains important thermodynamic information about the system.
Although I'm not exactly sure what you'll be going on to say in Part 2, I presume it will something to do with the effect of protein binding on heat capacity, which is linked in a complicated way to the changes in conformation and vibrational modes in the substrate and solvent. Therefore, it is crucial to get across the idea that heat capacity is related to the number of accessible modes that the system has for absorbing thermal energy.
I love your ideas. What do you all think about using my blog as a teaching tool. I want my students to think of science in multiple dimensions. Please check it out and comment.