I recently met Abe, a fellow physics nerd, at a board game night with friends. He helped me add to my physics-based Mindspace system (while doing the hard math for me), and generally helped me get excited about physics again. Physics, if you didn’t like that class in high school, is basically the code in which the physical universe is written. Since I think this stuff is awesomely cool, I asked Abe if he’d be willing to stop by the blog and explain Thermodynamics (heat transfer) for the geeks in the crowd. He graciously accepted.
Take it away, Abe.
Thermodynamics for Geeks
by Abe Abu-Madi
Thermodynamics, in a nutshell, is the transfer of energy between a given object, its surroundings and other objects. The laws of thermodynamics govern everything from the amount of heat given off by a Balrog to the average temperature on Tatooine. Let us take a look at what happens when Hollywood chooses to mettle in the affairs of physicists:
Tauntaun for Two
Let us pretend for a moment you are the hope of a galactic republic you have to save from an evil empire ran by your father’s boss. However before you can save anyone you are unexpectedly knocked unconscious by a Woompa and ultimately left to die in the frozen waste of Hoth. If this all sounds oddly familiar then I am either eagerly waiting your autobiography or you realize I am referring to the scene from Empire Strikes back.
In the movie Luke of course lives and with help from his father eventually brings balance to the force. How realistic is that though? The temperatures on Hoth supposedly go as low as negative 60° Celsius. Considering the average human body temperature is 37° Celsius that is very large difference. How plausible would it be for Luke to live? We’ll use Newton’s formula for heat transfer to get an idea how long it will take Luke’s body to drop to 20° Celsius. Why 20 degrees, you may ask? Anything less than 20° is profound hypothermia at which point Luke is assumed to be dead.
Newton’s equation is this
(1) T(t) = TA+(TH-TA)e-kt
T(t) = The temperature of the hot body at time t
TA = Temperature of the atmosphere
TH = Temperature of the hot body
t = time
k = cooling constant.
The constant k is most often gathered through measurements but we can’t go to Hoth so we’ll have to make a few assumptions. Let us assume on that particular night Hoth was at a crispy negative 45 degrees and that once every three minutes (180 seconds) Luke’s body temperature inside the Tauntaun goes down one degree. The equation then looks like this:
(2) 36 = -45+(37-(-45))e-k*180.
Solving for k then gives us a constant of k=.000068. We now have everything we need to see how long Luke would live under these conditions. Using 20° as the final temperature and our new cooling constant from equation 2, we plug our numbers into our original equation to give us:
Solving the equation for t gives 3408.27 seconds or 56.8 minutes. Assuming Luke’s body temperature was still at 37°Celsius when Han found him, Han would have less than an hour to prevent Luke’s body temperature from dropping and to warm him back up before he died. Han might prefer a blaster by his side but, for Luke’s sake I hope he is proficient with a shovel!
These are pretty generous conditions. If it is colder outside, Luke’s body temperature would go down faster, if the Tauntaun did not keep him as warm it would go down faster as well and most realistically if Luke’s body temperature was not at 37°Celsius at the time Han put him inside the Tauntaun (if he was already in a state of hypothermia), Han would have considerably less time. Han has less than a full hour to dig out a well insulated snow shelter to house two full grown men and begin warming Luke’s body. I hope Leia likes trips to swampy planets inhabited by little green hermits.
Predator or Prey
Well, after a chilling and probably lethal stay in Hoth, let us move to a more tropical location. In the 1987 movie The Predator (starring the Governator), Schwarzenegger’s character hides from the ultimate hunter in the galaxy, the Predator. The Predator has a type of thermal vision it uses to find its prey. In a flash of “brilliance” a mud covered Arnold hides among trees to hide his heat signature. Assuming there was no other issue than the his body heating the mud, his body would still heat the mud at such a rate that by the time the Predator was out of the water looking around the mud’s temperature would have changed enough to give off a noticeable heat signature and the Governator would have been another skull on his trophy wall.
What Schwarzenegger failed to realize about how heat transfer works is that when a higher energy particle interacts with a lower energy one some of the energy from the higher energy particle is transferred to the lower energy particle. When the type of energy we are talking about is in terms of temperature and heat, then the hotter particle becomes cooler and the cooler one becomes hotter. Arnold’s body would in fact lose heat, however the mud would gain it. The mud does not dissipate heat well and will continue to warm until it is at the same temperature as Arnold’s body. Once the mud and Arnold have reached the same temperature this particular system will be at equilibrium. In this context what equilibrium means is that when the particles from Arnold’s skin collide with the particles from the mud no energy is transferred. Once equilibrium is achieved then the mud and Arnold will share the same temperature and the Predator would see the mud on the outside of his body as him. A better way to hide from the Predator’s thermal vision would have been to hide Arnold’s body heat from escaping an enclosed area completely, which leads me to the next thermo dynamic movie mishap.
In the animated Japanese thriller movie Ghost in the Shell, the main character Major Kusanagi wears a type of thermal optic camouflage that comes in play often throughout the movie. Since the Major is a cyborg (in this case a fully machine body with an organic brain) trying to apply rules of body heat and temperature to her would be an exercise in futility! Instead, let’s talk about the group of full humans that wear the thermal optic camouflage in their riot gear later in the movie. Full humans should obey the laws of physics, right?
Let’s back up and talk about temperature. What does it mean for something to be hot or something else to be cold? In a simplistic case of dealing with matter it usually means how fast the particle is moving. Take a red rubber ball to be our single particle in question how fast said ball is thrown would determine what temperature it is measured at. More energy is a higher temperature. Keep in mind energy is transferred from a particle with more energy to a particle with less energy. This continues until equilibrium is reached or in other words all particles have the same energy.
So our task is to come up with a suit that makes its wearer invisible to thermal detection. Well from our previous discussion with the mud we know that simply putting something over the body of a person will not work for very long as the body will heat the object. The next logical step may be to use an object that dissipates heat easily like a copper heat sink. This may seem like a good idea until we realize that if the object dissipates heat at the same rate it is given to it, that the object will heat the surrounding atmosphere at the same rate as if it wasn’t there. Congratulations, your body is invisible however the air around you paints a giant thermal sign that says that says “Here I am!”
Instead let us prevent any energy our body puts out in the form of heat from escaping our newly made suit. We will pretend that our suit does not let any energy from the inside escape and it perfectly reflects energy from the atmosphere back (because otherwise in a warm area the suit would be colder than the surroundings and instantly visible). Another way to look at it is that we will make a mobile thermos that a person could fit and walk around in. Thermoses have been around for years–the inside stays the temperature of whatever is inside and the outside is (mostly) the temperature of the surroundings. So we have our working suit based on a concept we know works.
So what is the problem? In this case unlike coffee, a person still produces heat. With hot coffee, it has no way to create more energy so all it can do is transfer energy to its surroundings. A person on the other had will continue to produce body heat as long as they are alive. The air in the suit with the person will go from a comfortable level to unbearably hot in an extremely short amount of time. Using Newton’s formula for heat transfer, we can tell how long that will take. Say the temperature in the suit went up a full degree in the first minute and that k = .0645. Setting T(t) to 41°Celsius (the temperature at which heat stroke occurs), we can determine how long someone could wear the suit before they overcame by heat stroke, fell unconscious and died.
(1) T(t) = TA+(TH-TA)e-kt
Rewriting the equation to solve for t gives:
(4) t= [ln((T(t)-TA)/(TH-TA))]/-k
Putting in the numbers for the equations where:
T(t) = 41
TA = 42
TH = 37.
The solution given then is that t equals 122 minutes. So in just over two hours use of the suit heat stroke, unconsciousness and possible death would occur. For their sake I hope it is a short mission!
An Arab-American born and raised in the suburbs of Atlanta, Abe Abu-Madi is a physics and science fiction enthusiast extraordinaire. He has a Bachelor of Science in both physics and mathematics from Southern Polytechnic State University. He works in the Information Technology industry, and is fluent in both Arabic and math.