# Heat Quiz Explanations

Written: 2000.07.29
Last Revised: 2000.08.03

This document contains explanations of the quiz answers in the parent page (in case you're wondering why questions #7 and #9 are missing, I deemed them simple enough not to require discussion).

## Is heat a property of matter?

It is a popular miconception that heat is a form of energy which can be regarded as a property of matter. In fact, heat is not energy at all, and the term "heat energy" is not strictly accurate (although everybody uses it anyway because it's such a common colloquial term).

So what's the proper thermodynamic definition of heat? Don't bother looking it up in the dictionary; wordsmiths care more about colloquial definitions than precise technical definitions. You should look it up in a thermodynamics text instead, or if you don't have one, just read on.

As a preface, we must first explain the term "internal energy" (don't worry, you'll eventually understand why). At the microscopic level, we can define many types of energy that are associated with individual particles: we have kinetic energy, which is a function of mass and velocity. It can be kinetic energy of translation (movement through space), rotation (spin), or vibration (oscillation of molecules about their centres of mass). There are also various forms of potential energy, which are associated with nuclear, magnetic, and gravitational forces. There are dipole-moment energies associated with the miniscule electric currents of electrons orbiting around nuclei. And finally, there is mass-equivalence energy, as described by Einstein's famous equation E=mc².

But what about macroscopic objects? You might think you'd add up the energies of all the individual particles, but that's wildly impractical (to put it mildly). So we use a "cheat", and treat the object as if it's a single continuous piece of matter. For example, when we look at a baseball, we use its macroscopic velocity and mass to calculate its "kinetic energy". However, this means that the tiny, randomized motions of its molecules are not properly accounted for, so we need to invent a term to describe the energy of those randomized, internal motions. So what do we call it? Well, engineers and scientists are methodical and intelligent, but not particularly creative when it comes to naming conventions. We simply call it "internal energy." Many would call it "heat", but as we shall soon see, that is not strictly accurate.

The Definition of Heat

Unlike energy (internal or otherwise), heat is a strictly macroscopic concept. It has no meaning whatsoever at the microscopic level; an atom can be given energy but it can't be "heated". The concept of heat actually derives from our inability to deal with macroscopic objects and microscopic objects the same way. We split the energy of (for example) a baseball into organized kinetic energy and randomized "internal energy", and we must split organized and randomized methods of energy transfer as well, into work and heat.
Consider the following thought experiment: imagine a flash of warm liquid, sitting in an air-conditioned room. Beneath it, you can see an unlit bunsen burner. Inside it, you can see a stirrer which has been switched off. The liquid is warmer than the surrounding air, so it must have been heated, right? Wrong. The liquid is at an elevated temperature, indicating increased internal energy. But there is no way to tell whether this energy came from the bunsen burner or the stirrer. If it came from the bunsen burner, then it entered the liquid as heat. If it came from the stirrer, it entered the liquid as work. Once the energy is inside the liquid, there is no way to tell how it got there.
Therein lies the fundamental definition of heat: heat is not a property of matter, and it is not a type of energy. Heat is a type of energy transfer, just like work. You can perform work on an object, and it can experience an increase in internal or kinetic energy as a result, but it can't "contain" any work. Similarly, you can heat an object, but it can't "contain" any heat.

## Is temperature a property of matter?

Temperature is indeed a property of matter, but unlike internal energy, it is what thermodynamicists refer to as an intensive property, or state. This means that it is insensitive to the size or extent of the system. If you take a block of metal at 500 K and split it in two pieces, each piece has the same temperature regardless of size. The distinction between intensive and extensive states is important because intensive states are only relevant for equilibrium systems. Therefore, temperature is a property of matter but it only has meaning for systems in a state of thermal equilibrium.

So what is temperature? Well, you know it as the number which gives you a rough idea of how comfortable the air is, or the number on your oven that denotes its ability to cook a turkey. But everyone knows this is an oversimplistic definition, and sci-fi fans who fancy themselves self-taught physicists like to demonstrate their expertise by discussing a more fundamental definition of temperature. For this, they look to the formula ½mv²=1.5kT, where the left side of the equation is the average translational kinetic energy of an individual molecule and the right side contains k (the Boltzmann constant) and T (temperature in K). As a result, they tend to conceptualize temperature accordingly: they believe that temperature is defined as a function of average particle kinetic energy.

However, the above formula is part of the ideal gas law, and it is not the fundamental definition of temperature: it is a narrowly applicable approximation (very narrow; it's only accurate with plasmas and monatomic gases). So if we can't define temperature as a function of average particle kinetic energy, then what is it? For that, we must turn to the so-called "zeroth law of thermodynamics" (yes, I know, the name is dorky). The 0th law of thermodynamics states that if two systems are in thermal equilibrium, then they must be at the same temperature. Therefore, if two systems are not in thermal equilibrium, then energy must flow from the system with higher temperature to the system with lower temperature. Therefore, temperature is a pointer for the direction and rate of flow of energy as heat. Particle velocity has nothing to do with it.

For example, consider a black hole. It doesn't fall into any conventional definition of matter or energy. It is defined, at least in part, by the fact that its particles cannot escape even if their velocity appproaches c. But do we use hypothetical particle velocities to calculate its temperature? Of course not. Instead, we try to determine the point at which it reaches thermal equilibrium with its surroundings, and that is what defines its temperature.

PS. If you want a hardcore thermodynamics definition of temperature, here it is: if you take two systems which are not in thermal equilibrium and put them together, energy must flow between them until they reach a state of thermal equilibrium. At this point of equilibrium, entropy will be maximized (this is a consequence of the second law, which is used to define directionality of proceses). Therefore, you can find the point of equilibrium by setting dS/dr to zero, where S is entropy and r is the internal energy of the first system divided by the internal energy of the combined systems (the ratio of internal energies of the two systems is the only variable parameter if both systems are enclosed). A little bit of calculus leads to the formula T=1/(dS/dU), where U is the total internal energy of the system.

## Is it possible to build a perpetual motion machine?

Of course it's impossible to build a perpetual motion machine, but not everyone knows exactly why.

In order to explain, I must first describe what people mean when they say "perpetual motion machine". The minimum requirement for a perpetual motion machine is that it can maintain its operating process forever, even if it's a closed system. The particular type of process is irrelevant; it could be anything from the rotation of a flywheel to the movement of a reciprocating four-bar linkage or the circulation of an operating fluid.

So why can't we build such a beast? That's simple: we can't build it because it would violate the first and second laws of thermodynamics. The first law states that the total amount of mass/energy in a closed system must remain constant. The second law of thermodynamics states that entropy, once created, cannot be destroyed. There is no such thing as a perfect process, so any machine must create entropy as it works. In other words, even the minimum definition of a perpetual motion machine is impossible, because the second law guarantees that all of its useful energy will eventually turn into useless entropy, and the first law guarantees that there's no way to replace the lost useful energy of a closed system.

Some anti-scientific types might argue that it's reckless to say such a machine is impossible, and rattle off a laundry list of pessimistic statements about technology which have been proven wrong. But technological limitations and the laws of physics are entirely different things. There are many things which don't violate the laws of physics but which are technologically infeasible. For example, Lord Kelvin once claimed that heavier-than-air manned flight was impossible. He was right at the time, but we all know that he was eventually proven wrong. But was he talking about the laws of physics, or the limits of technology? Since birds are heavier than air and he must have seen some in his lifetime, he obviously knew that heavier-than-air flight does not violate the laws of physics, therefore he was talking about a technological limitations. Technological limitations often fall by the wayside, but never confuse them for violations of the laws of physics. The laws of physics don't fall quite so easily, and they don't permit perpetual motion machines.

## Is it possible to make a home heating system that pumps out 30 kW, draws only 8 kW, and doesn't need natural gas or any other sort of fuel?

Although the aforementioned heating system might seem to violate the first law of thermodynamics, it doesn't. Remember that the total amount of mass/energy in a closed system is fixed, but a house is not a closed system.

This means that the heating system doesn't need to take all of its energy from fuel or electricity; it can simply take it from the surrounding air. Imagine an air conditioning system in reverse, so that it cools the air outside your house instead of inside your house. Did you ever notice that the compressor outside your house blows out hot air? This is not just a hypothetical idea. It's called a "heat pump", and it's most often used in situations where electrical power is readily available but natural gas is not.

## Air at room temperature feels hotter or cooler depending on whether it's humid, dry, or breezy. Is this effect purely subjective?

Before we begin, remember that room temperature is much colder than the human body. Therefore, you are essentially an air-cooled bio-chemical machine. Your body makes heat, and the air carries it away (of course, it goes without saying that when the air temperature equals or exceeds your body temperature, your health is at risk).

Humidity affects the rate at which sweat will evapourate off your body. Air speed affects your convective heat transfer coefficient. Therefore, the suffocating sensation of humid air and the cooling sensation of a breeze are not purely subjective. In both cases, the conditions affect the rate at which energy flows in or out of your body, and that is a tangible, objectively meaningful quantity.

## Take a wooden bucket and a steel bucket, both at 25° C. Will one of them feel warmer than the other?

You don't need to be a thermodynamicist to figure this out. Just try it and you'll find that the wooden bucket indeed feels warmer than the steel bucket. But why? This isn't unique; for a more extreme example, preheat your oven to 80° C. Open it and immediately stick your hand inside. Warm but not dangerous, eh? Now, touch the metallic inner wall of the oven, just for an instant. Hot enough to cause pain, eh? But wait a minute ... the oven wall is at roughly the same temperature as the air!

How can this be? Why would one object feel hotter than another object at the same temperature? The explanation is that you cannot feel temperature. Temperature is an intensive equilibrium state of matter, but you're never in thermal equilibrium with room-temperature objects unless you're dead. You think you can feel the temperature of an object by touching it, but what you're actually feeling is heat flux.

The wooden bucket and steel bucket may be at the same temperature, but you will lose energy to the steel bucket faster than you lose energy to the wooden bucket. This is due to the thermal conductivity, density, and specific heat of steel, all of which greatly exceed the corresponding properties for wood.

Imagine a water tank with a hole in the bottom. If you widen the hole, raise the water level, or use a fluid denser than water, it will flow out quicker. Similarly, if you increase the thermal conductivity of an object, the difference between its temperature and your own, or its density and specific heat, you will increase the heat flux. In other words, a cold metal object will feel colder than a wooden object at the same temperature, and a hot metal object will feel hotter than a wooden object at the same temperature. In both cases, the thermophysical properties of metal will increase the heat flux between it and your fingers, thus fooling you into believing that it is actually cooler or hotter.

## Why do those damned chicken pot pies burn your mouth?

Contrary to popular belief, the chicken pot pie does not contain a supernatural substance that burns with the fires of Hell. Instead, it contains a viscous liquid interior whose specific heat is high but not outlandish. The secret is the pastry shell, not the liquid.

You see, the pastry shell completely encloses the liquid interior, and it has poor thermal conductivity. This has a twofold effect on the deadly tongue-destroying power of the dreaded chicken pot pie:

1. The shell acts as an insulator, trapping the heat inside.

2. The shell doesn't feel hot to the touch, so it lulls you into a false sense of security. If you are inexperienced with the Zen of chicken pot pie dining, you will take a big bite and blast half of your taste buds into oblivion.

## Fire-walkers can walk over hot coals at 400° C without injury. Is this an example of mind over matter?

If you understood all of the answers to the previous questions, then you should already know the answer to this one.

Fire-walking is not an example of mind over matter, because no supernatural forces are required to explain it. The temperature of the coals may be high, but there's nothing mystical about the coals or the firewalkers who run around on top of them. The coals are just pieces of dried softwood, and their ability to heat the soles of your feet is lower than you might expect, for the following reasons:

1. Their thermal conductivity is miniscule: well under ½ W/(m·K), compared to over 400 W/(m·K) for a good conductor such as copper. Thermal conductivity helps define the rate at which an object will heat a colder object, so low thermal conductivity means that the heat flux between the coals and the firewalkers' feet will be lower than you would expect from their temperature.

2. Their density is low: around 500 kg/m³ compared to nearly 9000 kg/m³ for copper. Their specific heat is actually 3 or 4 times higher, but that doesn't begin to make up for the 18x density disadvantage. This means that the so-called "thermal capacitance" of the coals is low, and the heat flux will drop quickly as the coals cool on the surface.

3. Their surfaces are rough. This reduces the contact surface area between the coals and the firewalkers' feet, as well as each other. This reduces the surface area available for heat conduction from the coals into the soles of the firewalkers' feet, thus reducing the amount of energy transfer for any given heat flux.

4. Their shapes are irregular. This further reduces the contact surface area between the coals and the firewalkers' feet, as well as each other.

To put it bluntly, all of the people who think that firewalkers require supernatural protection are either liars or morons (diplomacy was never my strong suit). If firewalking is mind over matter, then why don't they stoke up the coalbed until it shoots flames into the air? If firewalking is mind over matter, then why don't they use an aluminum hot-plate instead of a coalbed? If firewalking is mind over matter, then why do skeptics fare just as well as true believers? Firewalking mystics never even attempt to answer questions like that. Instead, they offer up pathetic objections such as "you can't prove that no mystical forces take part in the process." Obviously, they don't understand that if no mystical forces are required in order to explain firewalking, then there's no need to disprove their existence.

### Sources

• Fundamentals of Heat and Mass Transfer by Incropera and Dewitt, John Wiley & Sons, 1990.

• Engineering Thermodynamics by Reynolds and Perkins, McGraw-Hill, 1977.

• Fundamentals of Physics by Halliday and Resnick, Joyn Wiley & Sons, 1986.

This website is owned and maintained by Michael Wong
This site is not affiliated with Lucasfilm or Paramount
All associated materials are used under "Fair Use" provisions of copyright law.