Heat is not a noun

In thermodynamics, heat is not a noun. It’s a verb. This is confusing. Why? Because colloquially we think thermal energy and heat are the same thing, but in thermodynamics they are not. One is a noun and the other is a verb. Before diving into the weeds, let’s first acknowledge that nouns and verbs are labels. Keeping things simple: a noun labels a ‘thing’; a verb labels an ‘action’. Now we’re ready to define the two.

 

Thermal energy, from the chemical perspective, is the energy of molecular motion. The amount of thermal energy in a chemical system can be quantified by measuring its temperature. Thermal energy is a noun. This is confusing because its definition contains the word ‘motion’ that sounds verb-ish. Considering the two broad categories of kinetic energy and potential energy, thermal energy is more closely associated with kinetic energy, the energy due to motion.

 

Heat is the transfer of thermal energy. Heat is a verb because it involves the ‘action’ of transferring. This transfer of energy takes place spontaneously across a temperature gradient if a suitable pathway for the flow of energy is available. Heat is the flow, not the thing that flows. The thing that flows is thermal energy. The zeroth law of thermodynamics is about this flow: When a hot object is placed next to a cold object, thermal energy is transferred from the hot object to the cold one. The cold object is heated by the hot one. Simultaneously the hot object is cooled by the cold one. Heat is more closely associated with potential energy, as are other gradient-related energies such as gravitational (potential) energy.

 

But it’s hard to exclusively use heat as a verb. We easily slip into saying that ‘heat’ is transferred when something becomes hotter or colder. To repeat, heat is the transfer, not what is being transferred (which is thermal energy). In our minds, because of how we colloquially use the word ‘heat’, we associate it with temperature change – and thus conflate it with thermal energy. I tell my students to link thermal energy with thermometer (its measure). Thus, a change in thermal energy of an object leads to a change in its temperature. Many examples of heat-flow do lead to a change in temperature, but not always. Let’s look at three examples.

 

In the zeroth law example shown above, two objects at different temperatures are brought together. Spontaneously, the direction of heat-flow down the gradient is indicated by the red arrow. Both objects change temperature during the process. Finally, thermal equilibrium is reached. Both objects now measure the same temperature. The temperature gradient has been degraded – it no longer exists. We say that the two-object system has reached thermal equilibrium.

 

Chemists want to know about energy changes in a chemical reaction. In thermodynamics, we define the ‘system’ as the chemical substances. They have some energy content before the reaction, and after a chemical reaction (where chemical bonds have been made and broken) they often have a different energy content. We cannot easily measure the system’s change in energy directly, so we couple the system to what we call ‘thermal surroundings’ – typically modeled as an insulated water bath. If a chemical reaction releases energy (and most favorable reactions do), that energy is transferred to the water and when its temperature rises, we can calculate the rise in thermal energy of the thermal surroundings. A calorimeter is our device to measure this energy change. (An insulated water bath works well as a calorimeter, hence the model used!) This is illustrated below.

 

Students can quantify the heat by the formula q_therm = mCΔT where m is the mass of water, C is the specific heat capacity of water, and ΔT is the change in temperature of the water. All this is for the thermal surroundings. If the temperature goes up, ΔT is positive and therefore q_therm is also positive. But what about the system? Since the thermodynamic universe containing both the system and the surroundings is ‘isolated’, the energy gained by the thermal surroundings must have come solely from the chemical system. Thus, students learn that q_sys = –q_therm and energy is conserved. But heat is a verb. The noun that is used to represent the energy of the system is ‘enthalpy’. Textbooks and chemistry instructors often refer to it as ‘heat energy’ which is historically true (and noun-ish) but semantically confusing. This is why students have trouble with understanding the concept of state functions: enthalpy, the noun, is a state function; heat, the verb, is not.

 

A brief aside: I have skipped using the term ‘internal energy’ for the chemical system and ignored PV-work in the model of the thermodynamic universe, although I did draw the piston and shaft (in black) to represent it. Leaving PV-work out of the discussion, as I argue in a previous blog post, keeps this analysis cleaner and simpler for students.

 

In the model shown above, we only measured temperature changes in the thermal surroundings. The temperature of the system may or may not change. If we consider reactions solely carried out under ‘standard conditions’ so that we can tabulate standard enthalpies of formation, then we consider that the chemical reactants and their subsequent products to be at the same temperature. The system temperature didn’t change! But the temperature of the thermal surroundings might have. Thus heat-flow in this case only involves a temperature change in one milieu, not both. It makes sense to refer to q_therm as ‘heat’ because the thermal surroundings did change temperature, but for historical reasons, we still call q_sys ‘heat’ even though the system many not have changed in temperature. Why is there still an enthalpy change? The chemical bonds made and broken in the reaction have different enthalpies. In a typical ‘exothermic’ reaction, one that ‘releases heat to the surroundings’, weaker bonds are broken and stronger bonds are formed in the chemical system. Thus the system becomes more stable or lower in energy and ΔH, the change in enthalpy of the system, is negative.

 

Second aside: In some physical systems, students may be analyzing the opposite situation where the system is changing temperature, and exchanges energy with a thermal bath (which remains constant in temperature). For example, you could use a water bath to ‘heat’ a system as shown below. For that matter, you can consider a heating element in a reaction to act as such a reservoir of thermal energy.

 

In my final example, energy can change between the system and the surroundings without any change in temperature in either milieu. Consider the picture above where energy is being supplied by the thermal bath/reservoir to melt ice, the system, at zero Celcius. The ice receives energy and turns into liquid water at zero Celcius. Was thermal energy transferred? Hmm… no temperature change was involved. Historically we’ve come to call this ‘latent heat’. We don’t measure any temperature change although the word ‘heat’ is still invoked. In class, I avoid saying latent heat and simply refer to this as “delta-H of fusion” or ΔH_fus.

 

All this seems very clumsy. In class, I try to avoid using the phrase ‘heat of formation’ and use the more cumbersome ‘standard enthalpy of formation’. I get better every year but old habits die hard. I warn the students that they will often hear many of these enthalpies referred to as the “heat of [something]” even if there are no temperature changes. From a chemist’s point of view, I emphasize to students that when they think of ΔH, they should be thinking about changes in the strengths of chemical bonds (or interactions that fall under the rubric of “intermolecular forces”) – the old ones being broken and the new ones being made – in a chemical process. They shouldn’t think about heat per se.

 

This becomes doubly important when students begin learning about entropy. In any chemical reaction, there is an inherent entropy change. Here’s my brief one-paragraph version. If you’re utilizing a chemical reaction to do useful functional work (which may be different from PV-work), you may lose some of that energy as ‘heat’ to the thermal surroundings that isn’t due to inefficiencies in your apparatus (which may also be present). Rather, it is inherent to the chemical reaction. In the picture below, you want to minimize this ‘heat’ loss (the small double-headed arrow) and maximize the energy transfer from the system to functional work. In an equation, I would write this as ΔH = w’ + TΔS. As the enthalpy changes, the entropy changes (ΔS), and w’ (w-prime, to distinguish it from PV work) is the maximum useful work you could get out of the system, under ideal conditions. Students learn w’ as ΔG, the change in free energy of the system. When we talk about heat as the worst form of energy when it comes to utilization, we’re primarily referring to issues of entropy, not enthalpy.

 

I could go on, but this post has likely passed the TL;DR threshold. If you’re a student reading this, I hope this helped you. If you’re an instructor reading this, the take-home message is that when you use the word ‘heat’ in place of enthalpy in the context of thermodynamics, using it as a noun rather than a verb, you’re essentially using it as a label – a name – for a more abstract quantity. Your students hearing the word ‘heat’ might be associating it with temperature changes even if no such changes occur. Yes, I do want my students to use the phrases ‘endothermic’ and ‘exothermic’ correctly based on the sign of ΔH. But I want to drum into them that, conceptually, they should primarily associate ΔH in terms of the relative strengths of chemical bonds and interactions; that’s the system property chemists want to focus on! In thermodynamics, heat (unless being used as a more abstract label) is not a noun.